# Rational Functions and Asymptotes

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These questions are about simplifying and finding asymptotes and holes of rational functions.

[Rational functions and asymptotes] 25

Which of the following expressions is equivalent to

$\frac{x^{-2} y^3 z^{-4}}{x^{-3} y^5 z^5}$

A

$x^{2/3}y^{3/5}z^{-4/5}$

B

$xy^2z^9$

C

$x^{-5}y^8z$

D

$\frac{x}{y^2z^9}$

[Rational functions and asymptotes] 1

Compute: $\frac{x^2 + 7x + 12}{x^2 + 9x + 18} \div \frac{x^2 + 6x + 8}{x^2 + 15x + 56}$

A

$\frac{ (x+6)(x+2)}{ (x+7)(x+8)}$

B

$\frac{ x+6}{ (x+2)(x+7)(x+8)}$

C

$\frac{(x+7)(x+8)}{(x+6)(x+2)}$

D

$\frac{(2x+7)(7x+15)}{ 3(x+3)(x+6)}$

[Rational functions and asymptotes] 2

$\frac{x^2-2x-15}{x+3} =$

A

$x - 5$

B

$x^2 - 7$

C

$x - 7$

D

This cannot be simplified.

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