Simplifying Definition and 487 Threads

I am in grade 11 mathematics...i got this as a Thinking & Problem Solving Q..can someone simplify this, step by step? 4 - 1/x --------- 4 + 1/x THANKS!

Well here is the beginning of it: [-6(-4)^(n-1)] - 9 + [8(-4)^(n-2)] + 12 This is suppose to simplify to 2(-4)^2 + 3. But I have no idea how that 2(-4)^2 was obtained. Could anybody explain how that would work?

What does "simplify" means in this case: Simplify each of the following: 1. sin(3pi/2-x)

Started this today and I'm okay with simplifying radicals that don't include variables, but I'm having trouble solving ones with variables, like \sqrt{49y^{12}. I can't decide if I have to root it out like this \sqrt{7y^{6} times \sqrt{7y^{6} or just root it out the way it is since it is in...

let's consider this boolean logic experession: s=x'y'z+x'yz'+xy'z'+xyz can i simplify it to: s=x'y'z+x'yz'+xy'z' as xyz=1 where x,y,z in high logic(1) what's the simplest expression?

1. Express \frac{sin^2 2 \theta}{1+cos^2 2 \theta} as a function of sin \theta here's what I did: = \frac{4 sin^2 \theta cos^2 \theta}{1+(2cos^2 \theta -1)^2} = \frac{4 sin^2 \theta cos^2 \theta}{1+(4cos^4 \theta - 4 cos^2 \theta + 1)} = \frac{2sin^2 \theta cos^2 \theta}{2cos^2...

hey, i need to simplify this, and I am having a brain fart:confused: ...can u help me? f(x)= cosx(3cos3x) + (sin3x)(-sinx) i then have to find f(pi/6), but I am hoping i can do that once this is simplified... thanks Gill

Hi, i need help with simplifying this problem. I think it is an identity, but it looks very complex, and I wanted some other peoples thoughts/opinions. Well here goes... cos^2((pi/4)-(x-2)) - sin^2((pi/4)-(x-2)) I reduced it using the identity cos2x=cos^2x - sin^2x. I came out with...

Simplifying help please! Hi, I was given a double integral question and I managed to do the x integration. After placing the limits I get the following: ∫{ (2y²)(√2+y²) - (2y²)(√2y²) } dy I know the integrand can be simplified but I don't have a clue. Can anyone help? :confused: Thank...

okay I am supposed to prove the derivitive of: sqrt x/y + sqrt y/x is equal to y/x okay I am stuck where i have finally isolated y' i don't know how to reduce it further I am stuck with this at the moment (see attachment) can you please tell me the process you went through to simplify it?

I need to take the limit of this quotient as n goes to infinity: [2(-1)^(n+1) - 3^(n+1)] ----------------------- [2(-1)^(n) - 3^(n)] It seems to go to infinity over infinity in its current form, which, if I recall correctly, is indeterminate. It seems then that I need to simplify...

The determinate of the following 3x3 matrix 1-y, 2 , 3 2 , 4-y, 5 3 , 5 , 7-y gives a cubic that simplifies to, y^3 - 12*y^2 + y + 1 = 0. Now, apparently the teacher picked random numbers for the original matrix, making the problem delve into other realms of mathematics...

Apparently I've forgotten how to simplify algebraic fractions. I included the problem as a picture. http://community.webshots.com/photo/461491683/476214616XrKOZJ#" I can't figure out how they went from the red box and then to the green box and then the blue box. Obviously, I understand from...

I was just wondering if anyone has ever tried to make a new fundamental system for solving problems, ranging from Algebra to complex analysis and beyond in a more simplistic and less time consuming way?

there are two loops in an electrical circuit. I've got two equations and two unknowns. here are the equations v(t) = I1*R1 + 1/c*int(I1*dt) - 1/c*int(I2*dt) - first loop 0 = LdI2/dt + R2*I2 - 1/c*int(I1*dt) + 1/c*int(I2*dt) - second loop the capacitor is in the branch between the two...

Ok here is my problem, I am not sure how to simplify surds with additions and subtractions in them such as ones like this: http://img212.imageshack.us/img212/474/math010iz.gif At the moment I have managed to simplify it to this: http://img212.imageshack.us/img212/2011/math026eg.gif...

According to my text 7(x^3+4x)^6(3x^2+4) simplifies to: 7x^6(x^2+4)^6(3x^2+4) But it seems to me it should simplify to: 7x(x^2+4)^6(3x^2+4) What am I missing here? hk

hey, just a really quick question, any help wud be great, is it possible to simplify this radical further? p = sqrt root (6/70q^2) thx in advance for help.

log_x 4 + log_x 8 =5 I simplified that to log_x 32 = 5 but I can't get my head around what to do next and it's annoying me because I feel it's going to be something simple. :smile:

Hello I have to preform the operations and simplifying it. This is what i have \frac{1}{x}+\frac{1}{x-2}+\frac{3}{(x-2)^2} =\frac{3x^2-7x+8}{x(x-2)(x-2)} Is this correct?? Where do I go from here? Thanks P

0=\frac{cos^2x}{x}-\frac{1}{5} \frac{1}{5}=\frac{\cos x \cos x}{x} 5=\frac{x}{\cos x \cos x} 0=x \sec ^2 x-5 is this true? when I plot this, it doesn't give me the same function

here's the problem i want to find the net resistance. the only problem i think i have is that i don't know how to change the diagram so that the battery isn't in the middle of the circuit (i only know how to do questions where the battery is connected like a single complete path, which this...

i want to transform the black diagram into a series and parellel circuit (as u a see that the black diagram isn't exactly series or parellel). i made the two top left resistors into one (blue circle), and i want to do the same thing for the other two in green circle. however, if i make the top...

Simplify 1/2[Loga N - Loga (N - 1)] I get something like 1/2[Loga N / (N-1)] Loga root[ N / ( N-1 ) Loga root [ (N * ( N + 1)) / N^2 - 1 ]

I have an inequality: 1296(b^3) - 324(b^2) - 1008b + 108 > 0. I want to know for what values of b this inequality is true. Any suggestions?

no idea how to simplify this one: sqrt [1- [(x-1)^2/(x+1)^2]] thanks dave

well ill go through the whole question up to where i am (not very far) to make sure there were no prior errors, but i can't simplfy past where i am (maybe i just can't see it) Differentiate and simplify ...(1-x)^4 f(x) = -------- ...1-4x f'(x) = [4(1-x)^3(-1)](1-4x) - (1-x)^4(-4)...

Simplify in terms of cosine and sine only. tan^2x - {csc^2x\over cot^2x} From here, I assume you can flip the fraction and make it {tan^2x\over sin^2x} next, i reduce it to: (sec^2x-1) - ({sec^2x -1\over 1 - cos^2x}) and anyway..im lost; i don't know where to stop and how...

Technically this is a calculus problem I'm working on, but I'm just having problems with the Algebra portion. If I have: (\frac{1}{x\sqrt{1+x}} - \frac{1}{x}) How can I simply this so that I can substitute in 0 for x?

I am sorry for wasting your time with elementary mathematics but I can not complete my homework. (excuse the clutter, for I do not know how to use Latex) cube root ( -125 m^-4 n^5 ) I fully simplify this to: -5n/m * cube root (n^2 / m ) The answer is incorrect, wtf am I missing?

I am having trouble simplifying (4[(SQRT(x+2)) – (SQRT2))]/x I multiply the conjugate and I come up with 4/((SQRT(x+2)) + SQRT2) I'm not sure if I'm on the right track

Simplify sqrt(11+sqrt72)) + sqrt(11-sqrt(72)) better picture here http://members.rogers.com/agentj/images/math.jpg I don't know where to begin for this one, but apparently my calculator says the answer is 6 :redface:

How would I go about simplifying something like: (n+3)!/(n+1)! ?

can someone explain to me the stages that are missing in the expression in the attached picture. i think that it has to do with identities but in the book that i got it from did not explain clearly how they went from one line to another. i will appreciate the help very much.

I just don't get it, would anyone care to simplify the BCS theory for me? Please?

How do you expand and simplify this one? (2u+v).(u-2v) =2u.u+2u.(-2v)+v.u+v.(-2v) Where u and v are vectors and the "." is the dot. I did some but after this I am lost, how can I continue?

I am currently learning how to simplify trig functions, but is there a way to know which formulae to use? In my textbook there are three formulae: cos^2ttheta + sin^2theta = 1 1 + tan^2theta = sec^2theta cot^2theta + 1 = cosec^2theta I am also stuck in this question: prove this...