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Express as a single fraction: \(\frac{x}{x-2}-\frac{x+2}{x+3...

Express as a single fraction: $\frac{x}{x-2}-\frac{x+2}{x+3}$

A.

$\frac{2x^2 - 3x - 4}{(x-2)(x+3)}$

B.

$\frac{2x^2 + 3x - 4}{(x-2)(x+3)}$

C.

$\frac{2}{(x-2)(x+3)}$

D.

$\frac{ 3x + 4}{(x-2)(x+3)}$

E.

$\frac{3x - 4}{(x-2)(x+3)}$

View answer & explanation

Correct answer is D

$\frac{x}{x-2}-\frac{x+2}{x+3}$

$\frac{[x][x+3] - [x+2][x-2]}{[x-2][x+3]}$

= $\frac{x^2 + 3x - x^2 - 4}{[x-2][x+3]}$

= $\frac{3x - 4}{[x-2][x+3]}$

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