Fractions Definition and 604 Threads

Homework Statement \int\frac{e^xcos(log_7(e^x+9))}{(e^x+9)ln(7)}dx Homework Equations The Attempt at a Solution Let u= (ex+9) du= exdx New integral \int\frac{cos(log_7(u))}{(u)ln(7)}du This is where I got l little lost. Should I let log7(u)=\frac{ln(u)}{ln(7)}? Or is this...

Is there a free LaTex editor where you can click on a fraction button, and the fraction bar appears along with two empty boxes on top of and below it, representing the numerator and denominator? The LaTex editors that I've seen, when you click on the fraction button, just produce this...

Homework Statement Hi folks! :smile: This is just a conceptual question that has arisen during some reading. At one point the author states that for the reaction: CO_2 \leftrightharpoons X_{CO}CO + X_{CO_2}CO_2 + X_{O_2}O_2 where X is the mole fraction of each component at equilibrium...

Suppose that q(z) = 1, and p(z) = (1 + z)(1 + 3z). We wish to express q(z)/p(z) in the form where A and B are constants. To find them, we multiply through by p(z) = (1 + z)(1 + 3z) and obtain 1 = A(1 + 3z) + B(1 + z) = (A + B) + (3A + B)z Im fine up to this point, But according to...

Hello, I'm wondering what the reason for repeat linear factors in partial fractions is? I can't find an explanation online, they all just say do it!* I kind of understand why \frac{A}{x + 2} + \frac{B}{(x + 2)^2} can turn into ; \frac{6x + 7}{(x + 2)^2} Is there any...

Homework Statement \int(3x3-4x2-3x+2)/(x4-x2) Homework Equations P(x)/Q(x)=A1/(x-r1)+A2/(x-r2)+... if x-r occurs with multiplicity m, then A/(x-r) must be replaced by a sum of the form: B1/(x-r)+B2/(x-r)2+... I think this second equation is the source of my confusion. The Attempt at a...

Sorry if this is the wrong place to post. Kinda wanted to rant. I just wanted to express something that's been bugging me for a long time. Where does mathemaphobia really come from? I guess it's from how easy it is to get stuff wrong. If you're asked to discuss a poem, you can write some poop...

1.\int2x^2+x+9/(9x+1)(x^2+9) dx 2. (A/9x+1) + [(Bx + C ) / (x^2 + 9)] I get the worst numbers when I solve the system. The question is from an old exam and calculators are not allowed. Am I doing something wrong or is there another way to integrate this?

learning calculus here. got differential calculus, though it is a little foggy, and most of integral calculus, which is a little foggier. also using very unpolished precalc background, though i did give most of it a once-over. i have many questions which i can't think of, but of the top of my...

Hello! Quick question reagrding partial fractions. When there is a factor such as (x+2)3 in the denominator, then the fraction is separated into the components (x+2)1+...+(x+2)3. I am not convinced I understand quite why this is so. Partial fractions guides all offer something on the theme...

Homework Statement The question asks me to express the integrand in partial fractions to evaluate the integral \int \frac{13x-4}{6x^{2} -x -2} dx Homework Equations The Attempt at a Solution Well 6x² -x - 2 doesn't factorise (or I can't see it factorised). So I tried...

Homework Statement Hi, \int \frac{1}{x(x^{2}+1)}dx Homework Equations The Attempt at a Solution well I split this into partial fractions \frac{A}{x} + \frac{Bx + C}{x^{2} + 1} so 1 \equiv A(x^{2}+1) + (Bx + C)x when x = 0, A =1 when x = 1, Bx + C = -1 so...

Hello, I'm don't understand a step in the following integral: ∫(x-1)/(2x+1)dx = ∫(1/2)dx − (3/2)∫1/(2x+1)dx = (1/2)x − (3/4)ln|2x+1| + C The first step, where you get the 2 integrals ∫(1/2)dx and -(3/2)∫1/(2x+1)dx Where do (1/2)dx and -(3/2) come from? And where does (3/4) come...

Homework Statement Need to refresh my memory :-S Indefinite integral of x/(1+x^2) .. Homework Equations The Attempt at a Solution Would I use partial fractions on that bad boy?

question in fractions,,, how 2x+9/(3-x)(x+2) < 0 became (3-x)(x+2)(2x+9) < 0 " multiply both sides " zero is in the other side ,,,

\int \frac{2x+1}{4x^2+12x-7}dx \frac{1}{4} \int \frac{2x+1}{x^2+3x-\frac{7}{4}}dx \frac{1}{4} \int \frac{2x+1}{(x+\frac{3}{2})^2-4}dx u=x+\frac{3}{2} \frac{1}{2} \int \frac{u-1}{u^2-4}du \frac{1}{2} \int \frac{u}{u^2-4}du -\frac{1}{2}\int \frac{du}{u^2-4} \frac{1}{4}...

\int ln(x^2-x+2)dx \int ln( (x-\frac{1}{2})^2+\frac{7}{4} )dx u=x-\frac{1}{2} \int ln(u^2+\frac{7}{4})du uln(u^2+\frac{7}{4})-\int\frac{2u^2}{u^2+\frac{7}{4}}du uln(u^2+\frac{7}{4})-ln|u^2+\frac{7}{4}|+C (x-\frac{1}{2})ln(x^2-x+2)-ln|x^2-x+2|+C

Homework Statement \int \sqrt{tanx} dx The Attempt at a Solution I used the substitution u = sqrt(tanx), then x = arctan(x^2) so: 2 \int \frac{u^{2}}{u^{4} + 1} du = 2 \int \frac{u^{2}}{(u^{2} + 1)^{2} - 2u^{2}} =2 \int \frac{u^{2}}{(u^2 -\sqrt{2}u + 1)(u^2 +\sqrt{2}u + 1)} now...

I have no problem expanding brackets with fractions generally, unless the fraction contains an unknown variable, such as in the following expression: m/4[6m - 8] + m/2[10m - 2] I know that the answer is: 12/2m2 - 3m ..but I have no idea how to get to that. Can anyone help?

Alright... What are the rules for when the numerator (Top part) of the fraction has a higher degree than the lower part of the fraction. Something + {*} ... As in what is that SOMETHING based on the numbers? I have a midterm in like... 50 minutes and this is the only thing I need to know.

http://www.freeimagehosting.net/image.php?9722bd5444.png Link: http://www.freeimagehosting.net/image.php?9722bd5444.png" I've tried to used integration by parts and u substitution and I've also tried just multiplying the fraction by the denominator (6-x)^(1/2) but I am still confused at...

Homework Statement 1.) (a + 3b) /3ab + (a^2 b - 4ab^2) / 5a^2b^2 2.) n/(m^2) + 3/mn + 2/m 3.) Given F(x) = square root of x + 9 determine F(x+h) - F(x)/h 4.) say whether or not {(x,y) l x= y^2} is a function. Homework Equations The Attempt at a Solution im...

I remember learning that there is a mathematical method to converting decimals to the most accurate fraction. Can anyone refresh my memory??

Partial fractions of (-2x2+10x+8)/[x2(x+2)] I initally thought that it was A/x + Bx+C/x2 + D/x+2 but you really just do Ax+B/x2 + C/x+2 ...can anyone explain why the "x2" isn't split?

One way to add two fractions is to multiply the numerators of both fractions with each other's denominator, then adding the two products, gives us the numerator of the final result. Then we multiply together the denominators of each other--this gives us the denominator of the final result...

I have no difficulty with converting decimals to fractions generally (0.125 = 1/8) However, I am a bit stuck when it comes to converting a recurring decimals. My Math book tells me that 0.7777777r is not expressed as 77/100 as a fraction, but as 7/9. How do I calcuate that? Can anyone talk me...

I'm trying to do a question that requires the expansion of the following using partial fractions: f(z)=\frac{1}{(1+z^3)^2}. The fact that the bottom is squared is throwing me off for some reason... I've factorized the bottom, but I'm not sure whether I should use the complex roots or not, or...

Hi, had to learn partial fractions last year for laplace transforms, but have forgotten the general rules, and now i can't work out how to turn this into partial fractions: \frac{s}{\left(s^{2}+4\right)\left(s^{2}+9\right)}...

Let p be a prime number. Let A be an integer divisible by p but B be an integer not be divisible by p. Let A/B be an integer. How do I prove that A/B is divisible by p? This sounds like a simple question but I just can't get it. I'm doing it in relation to proving Fermat's little...

Homework Statement This problem is killing me. I need to bust this thing up using partial fractions. Homework EquationsThe Attempt at a Solution I'm leaning towards it being separated like this. Is this correct? If it is, I'm not exactly sure what I'm supposed to do next.

Homework Statement Sorry I don't have equation editor working 1/(z+1)(z2 + 2z + 2) Homework Equations The Attempt at a Solution (z2 + 2z + 2) z2 + 1) can be factor as (z - i)(z + i) However, I'm having trouble seeing the pattern on what (z2 + 2z + 2) would become, I...

how do you integrate 1/(x2 + 1)2 ? i have tried integration by partial fractions but when you set 1 equal to (Ax +B)(x2+1) + (Cx + D) this leads to A=B=C=0 and D=1 which just gives you the original equation

Hi Can anybody help me with these 3 problems?: 1) Express (3x-1)/(x+3)^2 in the form A/(x+3) + B/((X+3)^2) where A and B are constants. 2) A curve C has parametric equations: x=cost and y=2-cos2t (between 0 and pi) a)prove this can be expressed as the cartesian equation y=3-2x^2 b)...

I'm sure this is a no brainer to someone, but here it is.. what is does the partial fraction of this look like in expanded form? Or how can I make it fit on the table of laplace transforms? __(2s+1)__ (s-1)^2 + 1

Homework Statement I need to integrate this using partial fractions. "b/(x^2-a^2)" Homework Equations The Attempt at a Solution I have no idea where to begin.

Integration with partial fractions -- help! Homework Statement Here is the problem: http://img130.imageshack.us/img130/1673/integralthing.png The answer should be 4. Homework Equations N/A The Attempt at a Solution Here are my steps so far: (5x^2 - 17x + 10) / ((x-1)^3 *...

I really didn't know how to word the title so sorry if it's a little confusing. And I didn't know whether to post this in number theory or not but ah well. The other day, I started thinking about this and I was just wondering if it had been done before or if it's even correct; Half of all...

Homework Statement \int \frac{xdx}{x^3-1} Homework Equations The Attempt at a Solution Having difficulties with this one. I managed to break it down to two partial fractions, being x-1 and x^2+x+1 but couldn't make anything out of it.

Homework Statement Integral(sinx(x)dx/(cos^2(x)+cos(x)-2) Homework Equations The Attempt at a Solution What I tried to do first was factor the denominator, so i got (cos(x)-1)(cos(x)+2) from there, I set up my partial fractions equation trying to solve B(cos(x)-1) + A(cos(x)+2) =...

Homework Statement expand by partial fractions: Homework Equations 2(s+5)/(1.25*s^2+3s+9) The Attempt at a Solution ok I initially used the quadratic formula to get the two roots for the denominator these being (s+6/5+12i/5)(s+6/5-12i/5) i.e complex numbers so now the partial fractions...

Homework Statement A solution of ethanol (eth) and chloroform (chl) at 45°C with xeth = 0.9900 has a vapor pressure of 177.95 torr. At this high dilution of chloroform, the solution can be assumed to be ideally dilute. The vapor pressure of pure ethanol at 45°C is 172.76 torr. (a) Find the...

\int \frac{5x^2+11x+17}{x^3+5x^2+4x+20}dx \int \frac{5x^2+11x+17}{(x^2+4)(x+5)}dx \frac{Ax+B}{x^2+4}+\frac{C}{x+5}=\frac{5x^2+11x+17}{(x^2+4)(x+5)} (Ax+B)(x+5)+C(x^2+4)=5x^2+11x+17 Ax^2+5Ax+Bx+5B+Cx^2+4C=5x^2+11x+17 x^2(A+C)+x(5A+B)+(5B+4C)=5x^2+11x+17 A+C=5...

\int \frac{x^2+3x+1}{x^4+5x^2+4} (Ax+B)(x^2+1)+(Cx+D)(x^2+4) letting x=0 ..B+4D=1 not sure of the next move

\int \frac{x^3+6x^2+3x+16}{x^3+4x} dx \int \frac{x^3+6x^2+3x+16}{x(x^2+4)} dx \frac{x^3+6x^2+3x+16}{x(x^2+4)}=\frac{A}{x}+\frac{Bx+C}{x^2+4} x^3+6x^2+3x+16=A(x^2+4)+(Bx+C)x x^3+6x^2+3x+16=Ax^2+4A+Bx^2+Cx comparing coefficients.. A+B=6 , C=3 , A=4...

I wrote a program to convert decimals into fractions. It basically puts the decimal over the proper power of ten, and simplifies (at least, for nonreapeating fractions.) However, it uses a brute force method to find the LCD, and as a matter of aesthetics, I never like brute force. Does anyone...

Homework Statement \frac{dP}{dt}=P-P^{2} It seems that Partial Fractions should be used to solve this D.E., but I cannot find an example to go by. I even tried to rewrite the equation as: \frac{d}{dx}Y\left(x\right)=Y\left(x\right)-Y\left(x\right)^{2} But, that isn't helping me...

Homework Statement Compute the integral: int ((1-x^2)/(x^3+x)) dx Homework Equations int ((1-x^2)/(x^3+x)) dx The Attempt at a Solution I think I should use the partial fraction method to simplify the fraction so (1-x^2)/(x^3+x)= A/x + B/ (1+x^2) Therefore...

Homework Statement x^2 - 1/2x - 3/16 = 0 The Attempt at a Solution Actually, I don't know where to start since I have fractions.

1/(x+5)^2 (x-1) B=(-1/6) C=(1/36) I can't find the value of A, what method do you use to find it?

Here's (what I think is) a step in partial fractions that I don't understand: http://apthtml.com/images/partialfrac.png I'm taking the regular partial fractions steps and I keep ending up with 1 / (1 - x) rather than 1 / (x - 1). What am I doing wrong?