EDGE Math 8

Perform the indicated operations and simplify the resulting expression. Choose the correct answer.

1.	$\frac{3 x - 1}{x^{2} - 3 x - 10} + \frac{2 x + 5}{x^{2} - 4 x - 12}$

\frac{6 x^{2} - 21 x - 4}{(x - 5) (x + 2) (x - 6)}

\frac{5 x^{2} - 14 x + 21}{(x - 5) (x + 2) (x - 6)}

\frac{5 x^{2} - 24 x - 19}{(x - 5) (x + 2) (x - 6)}

none of the choices

Answer: $\frac{5 x^{2} - 24 x - 19}{(x - 5) (x + 2) (x - 6)}$

2.	$\frac{x + 5}{x^{2} - 6 x - 7} - \frac{6 x + 2}{x^{2} - 8 x + 7}$

\frac{- 5 x^{2} - 4 x - 7}{(x - 7) (x + 1) (x - 1)}

\frac{7 x^{2} + 12 x - 3}{(x - 7) (x + 1) (x - 1)}

\frac{- 5 x + 1}{(x + 1) (x - 1)}

none of the choices

Answer: $\frac{- 5 x^{2} - 4 x - 7}{(x - 7) (x + 1) (x - 1)}$

3.	$\frac{6 x + 1}{3 x^{2} y^{2}} + \frac{5 y + 2}{4 x y^{3}} - \frac{10}{8 x^{2} y}$

\frac{- 30 y^{2} + 18 x y + 8 y + 12 x}{24 x^{2} y^{3}}

\frac{3 y^{2} + 78 x y + 8 y + 12 x}{24 x^{2} y^{3}}

\frac{- 15 y^{2} + 39 x y + 4 y + 6 x}{12 x^{2} y^{3}}

none of the choices

Answer: $\frac{- 15 y^{2} + 39 x y + 4 y + 6 x}{12 x^{2} y^{3}}$

4.	$\frac{4}{x + 1} + \frac{6}{x^{2} - 1} - \frac{3}{x - 1}$

\frac{4 x + 4}{(x + 1) (x - 1)}

\frac{4}{x - 1}

\frac{1}{x + 1}

none of the choices

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

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

\frac{- 5 x^{2} + 15 x - 6}{(x - 1) (x - 2) (x - 3)}

\frac{2 x^{2} + 25 x - 18}{(x - 1) (x - 2) (x - 3)}

\frac{- 5 x + 2}{(x - 1) (x - 2)}

none of the choices

Answer: $\frac{- 5 x^{2} + 15 x - 6}{(x - 1) (x - 2) (x - 3)}$

6.	$\frac{1}{x - 4} - \frac{5}{x + 5} + \frac{2}{x - 6}$

\frac{- 2 x^{2} + 51 x - 190}{(x - 4) (x + 5) (x - 6)}

\frac{8 x^{2} + 49 x - 50}{(x - 4) (x + 5) (x - 6)}

\frac{- 3 x^{2} + 53 x - 110}{(x - 4) (x + 5) (x - 6)}

none of the choices

Answer: $\frac{- 2 x^{2} + 51 x - 190}{(x - 4) (x + 5) (x - 6)}$

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