1
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1answer
44 views

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 ...
1
vote
1answer
131 views

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.
1
vote
3answers
27 views

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 ...
0
votes
2answers
38 views

What is the common denominator

Help me find the common denominator please! Thank you Here it is : $$\dfrac{5}{3x+2}-\dfrac{3}{3x-2}=\dfrac{7}{6x-4}+\dfrac{x+4}{18x^2-8}. 1$$
1
vote
1answer
58 views

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 ...
1
vote
1answer
25 views

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 ...
3
votes
3answers
47 views

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 ...
0
votes
2answers
46 views

Find asymptotes of $(2x)/(x-1)^2$

What are the asymptotes of $$\frac{2x}{(x-1)^2}$$ ? I have problems already on domain.
2
votes
2answers
184 views

Permutations and Cross-ratios

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, ...
0
votes
3answers
15k 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 ...
0
votes
1answer
478 views

Rational function to find minimum surface area of cylinder

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 ...