What is Simplifying: Definition and 498 Discussions

Simplified Chinese characters (简化字; jiǎnhuàzì) are standardized Chinese characters used in Mainland China, Malaysia, and Singapore, as prescribed by the Table of General Standard Chinese Characters. Along with traditional Chinese characters, they are one of the two standard character sets of the contemporary Chinese written language. The government of the People's Republic of China in mainland China has promoted them for use in printing since the 1950s and 1960s to encourage literacy. They are officially used in the People's Republic of China and Singapore, while traditional Chinese characters are used in Hong Kong, Macau, the Republic of China (Taiwan) as well as South Korea to a certain extent, and occasionally in the Chinese community of Malaysia and Singapore.
Simplified Chinese characters may be referred to by their official name above or colloquially 简体字; jiǎntǐzì. In its broadest sense, the latter term refers to all characters that have undergone simplifications of character "structure" or "body", some of which have existed for millennia alongside regular, more complicated forms. On the other hand, the official name refers to the modern systematically simplified character set, which (as stated by then-Chairman Mao Zedong in 1952) includes not only structural simplification but also substantial reduction in the total number of standardized Chinese characters.Simplified character forms were created by reducing the number of strokes and simplifying the forms of a sizable proportion of Chinese characters. Some simplifications were based on popular cursive forms embodying graphic or phonetic simplifications of the traditional forms. Some characters were simplified by applying regular rules, for example, by replacing all occurrences of a certain component with a simplified version of the component. Variant characters with the same pronunciation and identical meaning were reduced to a single standardized character, usually the simplest amongst all variants in form. Finally, many characters were left untouched by simplification and are thus identical between the traditional and simplified Chinese orthographies.
A second round of simplifications was promulgated in 1977, but was later retracted in 1986 for a variety of reasons, largely due to the confusion caused and the unpopularity of the second round simplifications.In August 2009, the PRC began collecting public comments for a modified list of simplified characters. The new Table of General Standard Chinese Characters consisting of 8,105 (simplified and unchanged) characters was officially implemented for use by the State Council of the People's Republic of China on June 5, 2013.

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  1. P

    Trigonometric Equation Simplification Strategies

    Homework Statement (sec^2 x - 1)/(sin^2 x) Homework Equations The Attempt at a Solution i know that the answer is sec^2 x, but i have no idea what steps to take to get there
  2. S

    Can Ln and Logarithmic Expressions Be Further Simplified?

    is it possible to simplify this more?? Ln(log7-log76)= Ln(log77)
  3. R

    How Do You Simplify Complex Fractions with Nested Radicals?

    Homework Statement \frac{1 + \sqrt{\frac{1}{1 + \left(\frac{s}{u}\right)^{2}}}}{1 - \sqrt{\frac{1}{1 + \left(\frac{s}{u}\right)^{2}}}} Should equal \left(\sqrt{1 + \left(\frac{u}{s}\right)^2} + \left(\frac{u}{s}\right)\right)^{2} Homework Equations above The Attempt at a Solution...
  4. M

    Understanding Complex Numbers: Squaring and Simplifying

    Hey guys. So, complex numbers. Its been a while since I've dealt with them. I've been wondering a few things about them. When expressed in the form a + ib, is there a particular way that you square them? And when you have a rational number, with an i term on the bottom, how exactly...
  5. L

    Simplifying Trig Homework Statement | Limit x-->0 for (secx-1)/x^2

    Homework Statement (secx-1)/x^2 limit x--->0 Homework Equations secx=1/cosx (1-cosx)/x=0 The Attempt at a Solution I have done obvious thing, solved to make secent cosine and got common denominators in the top portion of the fraction, then subtracted. Ended up with...
  6. D

    How to Simplify a Derivative with Multiple Terms

    Homework Statement Find the derivative of f(x)=2x^3+cos^2(x^3) The Attempt at a Solution f'(x)=6x^2+2cos(x^3)*-sin(x^3)*3x^2 f'(x)=6x^2-6x^2cos(x^3)sin(x^3) The book has a different solution since they always simplify, but how would I simplify it? I know it has something to do...
  7. B

    Simplifying |x|-|x-6|: A Math Tutorial

    How could I go about expressing |x|-|x-6| without using absolute value signs?
  8. Somefantastik

    Equation of Diffusion, trouble simplifying, PDE

    isotropic equation, so k, ρ, and c are constant, where k is thermal conductivity, c is specific heat, and ρ is the density of the body. the equation boils down to \left( \frac{c\rho}{k}\right) \left(\frac{\partial u}{\partial t}\right) - \left(\frac{\partial^{2} u}{\partial...
  9. M

    Problem simplifying an equation

    Homework Statement What is the steps between the two equations? Homework Equations P = a^{2}P+b^{2}P^{2}/(P+1) \Rightarrow P^{2}-(a^{2}+b^{2}-1)P-b^{2} = 0 Thanks!
  10. C

    Simplifying Radicals with a Simple Program

    Hello. I wrote a simple program that helps me simplify radicals: #include <iostream> #include <math.h> typedef struct { unsigned int x, y; }pair; bool breakcube(unsigned int radi, unsigned short inx, pair& pr) { unsigned int cb = 0; for (unsigned int i = 2; i < radi; i++) { cb=i...
  11. L

    Algebra Question: Simplifying Ration Questions

    Alright It's been a while since I did algebra and now I'm getting back into it in honors algebra 2 (shakes head) [high school]. Anyways I got a question on factoring numerators. 6x^{2} + 7x + 2 ------------- 4x^{2} - 1 I don't know where to start, if someone can be a guidance this would...
  12. 3

    Simplifying Trig Expression: (sec(t) - cos(t))/sec(t) = (f(t))^2

    Homework Statement Simplify and write the trigonometric expression in terms of sine and cosine: (sec (t) - cos (t))/sec (t) = (f(t))^2 Homework Equations sec (t)=1/cos (t) The Attempt at a Solution (sec (t) - cos (t))/sec (t) = ((1/cos (t))-cos(t)) / (1/cos (t)) =...
  13. R

    Simplifying Expression to tan $\frac{\alpha}{2}$

    Homework Statement Prove \frac{sin 2 \alpha}{1+cos 2 \alpha}-\frac{cos \alpha}{1+cos \alpha}=tan \frac{ \alpha}{2} Use half and double angle formulas, I get; The given expression is equal to: \frac{(2 tan \frac{\alpha}{2})(1+tan^{2}...
  14. P

    Simplifying a trigonometric expression

    cos(4x) + \sqrt{2}cos(3x) + cos(2x) = 0 --------------------------------------------------- Ok, so break down everything to a double angle and i get: 2cos^2(2x) - 1 + sqrt(2)*(sqrt((cos(2x) + cos^2(2x))/2) - sqrt((1-cos^(2x)*(1-cos(2x))/2) + cos(2x) = 0 ...which is quite complicated to...
  15. P

    How can complex numbers be simplified?

    Homework Statement Simplify (1+i\sqrt{2})^5-(1-i\sqrt{2})^5 Homework Equations z=a+bi z=r(cos\varphi+isin\varphi) tg\varphi=\frac{b}{a} r=\sqrt{a^2+b^2} The Attempt at a Solution...
  16. K

    Simplifying Summations: Finding a Solution for a Tricky Problem

    Homework Statement I'm trying to simplify a summation. I have something that looks like \sum \sqrt{(1/4)(i)} (1/4) Granted I might have made a mistake setting this up which would make my question irrelevant but anyway. Homework Equations there are equations for i, i squared and i cubed The...
  17. H

    Simplifying a arc length problem

    Simplifying an arc length problem I have L= Int(-2..2) sqrt(16*cosh(4*t)^2+9*sinh(4*t)^2+9) and can use Maple to simplify this to sqrt(25*cosh(4*t)^2) but I just can't see how that is done. (or how to get maple to show me the steps!) Can anyone help by showing the steps, including any...
  18. R

    Simplifying a sum with fractions of products of binomials

    Homework Statement 1/(a-b)(a-c) + 1/(c-a)(c-b) + 1/(b-a)(b-c) Homework Equations Is there a way to simplify this? If I start multiplying out everything to get the LCD my final answer will be huge. The Attempt at a Solution As I said, without somehow simplifying it at the start...
  19. R

    Algebraic expressions - simplifying

    Hi all, I'm retaking the GRE soon and I keep making stupid algebra mistakes in my calculus problems so I'm going through a textbook from 1965 that is helpful but has me stumped on some problems. I hope someone can steer me in the right direction. 1/(a-b)(a-c) + 1/(c-a)(c-b) +...
  20. R

    Simplifying a trigonometric binomial

    Is this correct? (bcos30-85.7)(bcos30-85.7)=b²cos²30-85.7cos30-85.7bcos30+85.7²
  21. I

    Question about simplifying this equation

    tan x/sin x + 1/cos x The choices are A. 2tan^2x B. 2cosx C. 2cosx-1 D. 2secx Do I make the tan sin/cos and multiply by reciprocal of sin? I did that and end up with 1/cos + 1/cos
  22. B

    Simplifying (2/6 -root3)^2 - (2/6+root3)^2

    im having trouble trying to figure out a problem. can someone help me. (2/6 -root3)^2 - (2/6+root3)^2 if that makes sense to anyone help. I think that the denominator of both has to be rationalised but do i expand the squared brackets first or later or what? any ideas welcome thanks
  23. R

    Simplifying Summation and Factorial

    I was looking at the web page containing a derivation for the Poisson distribution: http://en.wikipedia.org/wiki/Poisson_distribution which derives it as the limiting case of the binomial distribution. There is a simplification step which I am missing, which is the step(s) between...
  24. U

    Find f'(x) Two Ways: Product/Quotient Rule & Simplifying

    Homework Statement Find f '(x) two ways: By using the product or quotient rule, and by simplifying first. f(x) = ((x^3) + 9)/ (x^3) Homework Equations f '(x)= (G(x) * F '(x) - F(x) * G '(x)) / [G(x)^2] The Attempt at a Solution f...
  25. A

    Solve Integral: y=(1-x^{2/3})^{3/2}, 0\leqx\leq1

    Hello Here is an integral question I have. It's a surface area problem, but i just have issues simplifying the square root before solving. Any help appreciated! y=(1-x^{2/3})^{3/2}, 0\leqx\leq1 My work: dy/dx=-x^{-1/3}(1-x^{2/3})^{1/2} (dy/dx)^{2}=-x^{-2/3}(1-x^{2/3})...
  26. N

    Simplifying a Sum of Squared Terms: A Geometric Series Approach

    Homework Statement How can I simplify sum from j=0 to infinite of x^(2j) ? Homework Equations The Attempt at a Solution THis is close to the geometric series but I'd have to square each individual term
  27. K

    Simplifying Equation With Square Root

    Homework Statement An equation in a book lists this equation: (c - 18)^{2} = (-3\sqrt{c})^{2} And it simplifies it as: c^{2} -45c + 324 = 02. The attempt at a solution When I do out the equation, I get: c^{2} + 324 = 9 + c i squared c, then -18 for the left side of the equation, then for the...
  28. C

    Simplifying with Pythagorean identites.

    Homework Statement Simplify: 2csc^2 - csc^4 + cot^4 Homework Equations The Attempt at a Solution 2(1/sin^2) - 1/sin^4 + cos^4/sin^4 So here, i figured that if i re-write them, that maybe it will leave me more options, but I don't see anything that will cancel out. Then i...
  29. M

    How to Simplify These Complex Boolean Algebra Equations?

    Homework Statement Simplify these equations and functions 1. xyz’ + x’ (x + z) + x’yz + x’y’z’ 2. xy (z + z’) + x’y’z 3. wxyz + w’xy’z + wx (y’ + z) + w’x’z 4. F(A, B, C, D, E) = ∑(0, 1, 5, 6, 13, 15, 20, 21, 22) 5. F(w, x, y, z) = ∑(0, 1, 2, 3, 11, 13, 15) Homework Equations...
  30. J

    How can I simplify this expression using factoring?

    Homework Statement Show 2a^2*b^2*c^2 + (a+c)^2*(a+b)^2*(b+c)^2 - a^2*c^2(a+c)^2 - (a+b)^2 * a^2 * b^2 - (b+c)^2*b^2*c^2 = 2abc(a+b+c)^3 Homework Equations The Attempt at a Solution Well I actually tried to expand all of the exponential terms but that ended up being a total...
  31. D

    Simplifying: \frac{x^2-6x+4}{(x^2-4)(x-2)}

    How do I simplify this? \frac{1}{x-2} - \frac{1}{x^2-4} = \frac{(x^2-4)-(x-2)}{(x^2-4)(x-2)}
  32. K

    Simplifying equations using boolean algebra

    [b]1. Simplify the following equations using boolean algebra [b]2. a) abc + ab'c'+ ab'c b) (abc)'+(a+c)'+b'c' [b]3. Please help me to solve the above equations
  33. P

    Simplifying a Trig Equation: Finding the Zeros

    Homework Statement (this is really only part of my problem it's an optimization problem but this is where I'm stuck) Find the zeros of: cos^2(x)-sin^(x)+cos(x) Homework Equations The Attempt at a Solution I've been trying to use trig identities such as sin^2 + cos^2 = 1 but it's...
  34. V

    Current and potential difference, simplifying circuit diagrams

    [SOLVED] current and potential difference, simplifying circuit diagrams Consider the circuit shown in Figure P31.69, in which RA = 25 and RB = 7 . Tabulate the current through, and the potential difference across, each resistor. Figure P31.69 resistor current (A) potential...
  35. F

    How simplifying this ratio test for series?

    [SOLVED] How simplifying this ratio test for series? Basically, we are asked if (n!n^2)/(2n)! converges absolutely... I got to the point where lim as n --> infinity of [(n+1)!(n+1)^2]/(2(n+1))! X (2n)!/n!n^2 by the ratio test. But I don't know how to manipulate the factorials...
  36. L

    Simplifying this equation

    w=\frac{k}{1-n}(v^{1-n}_{2}-v^{1-n}_{1}) let k=pv^n \frac {p_{2}v^{n}_{2}v^{1-n}_{2} - p_{1}v^{n}_{1}v^{1-n}_{1}}{1-n} how can this become w=\frac {p_{1}v_{1} - p_{2}v_{2}}{n-1} thanks
  37. R

    How to Simplify the Expression sin60° + sin20°?

    [SOLVED] Simplifying Trig Products Homework Statement Express the following as a product and simplify. sin60° + sin20° Homework Equations The Attempt at a Solution I don't understand what the question is trying to say. For example, do I convert sin60° and then add. I don't...
  38. A

    Solving Equation for Lambda in Terms of A

    I am trying to solve for the variable lambda in terms of A. After multiplying the denominator term over to the other side, how do I go on from there? I don't know how to get rid of the exponential terms. Thanks on advance. http://img521.imageshack.us/img521/4006/picture1ug1.th.png
  39. J

    Simplifying a solution such that the imaginary number goes away

    Homework Statement Given a general solution to a system of differential equations: Y(t)= C1(1;2i)e^(2it)+C2(1;-2i)e^(-2it) side note: i is sqrt of -1, and the (1;2i) is a 2 by 1 matrix. The idea is to simplify the solution such that the imaginary components go away. Homework...
  40. F

    Simplifying a differentiation problem

    Homework Statement [3x^2 + 2(sqrt x)] / x My book says it simplified it to: 3x + 2x ^-1/2I understand the 3x part since 3x^2/x = 3x But where did the second part come from? I tried to make sense with the power rule but it still doesn't seem clear to me. Anyone get it?
  41. M

    Simplifying Trig Expressions and cofunctions

    Homework Statement Sec^2x X cotx --------------------- csc xAlso, if anyone wants to explain cofunction identities and how to use them, to be that would be very much appreciated. Homework Equations The Pythagorean identities as well as the basic identities of trig functions. Any...
  42. B

    Simplifying a product of sin functions

    can someone please simplify? \sin \frac{\pi}{n} \sin \frac{2\pi}{n} ... \sin \frac{(n-1)\pi}{n}
  43. G

    Simplifying a fraction as a surd?

    Simplifying a fraction as a surd?? If I have a rather large fraction such as 115/36 there is no obvious way of cancelling this, but is there a way of expressing it as a surd?
  44. A

    Reducing a Complex Equation: Steps and Solutions

    Does anyone know the steps involved in reducing ((1+u/c)/(1-u/c))^0.5 - 1 = u/c ?
  45. A

    Trouble Simplifying Homework Equations

    Homework Statement I am reviewing some old exam solutions and came across something I cannot figure out. I'm don't understand how they simplify from the first equation to the second. I looked up a table of trig identies but could not find anything that would help. Homework Equations...
  46. P

    Reducing Factorials: Is the Answer 1/[2n*2n+1]?

    Homework Statement (2n-1)!/(2n+1)! Homework Equations The Attempt at a Solution ...2n-2*2n-1 ------------ (pretend that's a divider) ...2n-2*2n-1*2n*2n+1 Is the answer 1/[2n*2n+1]?
  47. R

    Simplifying a recursive function

    I am trying to find a formula for f(x) = a*f(x-1) + b*f(x-2) for x≥1, assuming f(-1) and f(0) are known. In other words, I need some expression for f(x) just in terms of a, b, f(-1), and f(0). I tried plugging in stuff and factoring on paper for the first few iterations, but it quickly got out...
  48. K

    How Do You Simplify the Expression \(\frac{a^4-b^4}{4a^2+4b^2}:(a+b)\)?

    I'm supposed to simplify this, help please! \frac{a^4-b^4}{4a^2+4b^2}:(a+b) Sorry for posting in the wrong section, could someone move it?
  49. T

    Simplifying Trigonometric Expressions

    Without using a calculator This is part of a GCSE maths question from a non-calc paper How does \frac{25\pi}{3}-\frac{25}{2}sin120 become simplified?
  50. B

    Solving Log Equations: No Simplification Needed

    Hi, To solve the following d.e.: xdy-ydx = 0 1 you get ln(y)-ln(x)=C 2 no clearly you can simplify to: ln(y/x)=c 3 which after taking exponentials gives: y=Ax where A=e^c 4 however what interests me is if you do not simplify...
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