Rational Functions and Asymptotes
Rational Functions and Asymptotes

Rational Functions and Asymptotes

Lead Author(s): Kelly Cline

Student Price: FREE

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

x2y3z4x3y5z5\frac{x^{-2} y^3 z^{-4}}{x^{-3} y^5 z^5}

A

x2/3y3/5z4/5 x^{2/3}y^{3/5}z^{-4/5}

B

xy2z9 xy^2z^9

C

x5y8z x^{-5}y^8z

D

xy2z9 \frac{x}{y^2z^9}

[Rational functions and asymptotes] 1

Compute: x2+7x+12x2+9x+18÷x2+6x+8x2+15x+56\frac{x^2 + 7x + 12}{x^2 + 9x + 18} \div \frac{x^2 + 6x + 8}{x^2 + 15x + 56}

A

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

B

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

C

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

D

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

[Rational functions and asymptotes] 2

x22x15x+3=\frac{x^2-2x-15}{x+3} =

A

x5x - 5

B

x27x^2 - 7

C

x7x - 7

D

This cannot be simplified.

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