# Tagged Questions

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### expand a rational function in a power series

$$\frac{4-x}{(2-x)(1-x)^2}$$ Expand in ascending powers of x, stating when the expansion is valid; also write down the coefficient of $x^n$
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### Solve this simple polynomial

$$\text{Problem: }{x^3-x^2-x-2 \over x^2 + x - 6}$$ My textbook was able to come up with $(x-2)(x^2+x+1)$ $$\text{Textbook: }{(x-2)(x^2+x+1) \over (x-2)(x+3)}$$ I've tried grouping and using the ...
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### How to evaluate $\int_0^1\frac{1+x^4}{1+x^6}\,dx$

$$\int_0^1\frac{1+x^4}{1+x^6}\,dx$$ Can anyone help me solve the question? I am struggling with this.
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### I am not sure if the answer for the dividing rational expressions problem (attached) should be simplified

$$\frac{x}{x+2} \div \frac{1}{x^2 - 4}$$ Original image: http://i.stack.imgur.com/EEqd4.jpg -I am not sure if the answer for the problem (which is attached) would be $\frac{x^3-4x}{x+2}$ or if it ...
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### What is the common denominator

Help me find the common denominator please! Thank you Here it is : $$\dfrac{5}{3x+2}-\dfrac{3}{3x-2}=\dfrac{7}{6x-4}+\dfrac{x+4}{18x^2-8}. 1$$
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### Prove that there is no rational function in $F(x)$ such that its square is $x$

I came across this homework problem and honestly have no idea where to begin. Prove that there is no rational function in $F(x)$ such that its square is $x$. First of all, I am confused about ...
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### Ring of rational functions ideal generators

There is an affine variety $X\subset \mathbb{A}^n$ with its ring of rational functions which is the quotient ring of $\mathbb{k}[X]$ (each $f\in \mathbb{k}(X)$ has a form $\frac{p}{q}$ where $q$ does ...
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### Determining the positioning of rational functions without plotting points

When graphing rational functions, how do I determine the orientation of a rational function around the asymptotes without plotting points? For example, is it possible to determine which one of these ...
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### Find asymptotes of $(2x)/(x-1)^2$

What are the asymptotes of $$\frac{2x}{(x-1)^2}$$ ? I have problems already on domain.
Pick four distinct numbers, list all 24 permutations, and compute the cross-ratio of each permutation. Show that at most six numbers have occurred, given by the cross-ratio group $y, \frac{1}{y}, 1-y, ... 3answers 18k views ### Finding the range of rational functions I have a problem that I cannot figure out how to do. The problem is: Suppose$s(x)=\frac{x+2}{x^2+5}$. What is the range of$s$? I know that the range is equivalent to the domain of$s^{-1}(x)\$ but ...
I have developed the formula to determine the radius of a cylinder with a fixed volume: $$f(x) = \sqrt[3]{\dfrac{V}{\pi}}\$$ Substituted into the formula for the surface area of a cylinder, I get ...