EDGE Math 8

Simplify each complex rational expression. Choose the correct answer.

1.	$\frac{8 - \frac{1}{x^{2} - 2 x + 1}}{\frac{7 - 16 x + 8 x^{2}}{x^{2} - 1}}$

\frac{1}{x - 1}

\frac{x + 1}{x - 1}

\frac{1}{x + 1}

none of the choices

Answer: $\frac{x + 1}{x - 1}$

2.	$\frac{\frac{1}{x} + \frac{2}{x^{2}} - \frac{3}{x^{3}}}{\frac{x^{2} + 4 x + 3}{x^{3}}}$

\frac{x - 1}{x + 1}

\frac{1}{x - 1}

\frac{1}{x + 1}

none of the choices

Answer: $\frac{x - 1}{x + 1}$

3.	$\frac{x^{- 2} + y^{- 2}}{3 x^{- 1} y^{- 1}}$

\frac{x^{2} + y^{2}}{3 x y}

\frac{3 x y}{x^{2} + y^{2}}

\frac{3 (x^{2} + y^{2})}{x y}

none of the choices

Answer: $\frac{x^{2} + y^{2}}{3 x y}$

4.	$\frac{a^{- 3} + b^{- 3}}{a + b}$

\frac{a^{3} b^{3}}{a^{2} - a b + b^{2}}

\frac{a^{2} - a b + b^{2}}{a^{3} b^{3}}

\frac{a^{3} b^{3}}{a^{3} + b^{3}}

none of the choices

Answer: $\frac{a^{2} - a b + b^{2}}{a^{3} b^{3}}$

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