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.

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

Correct answer is D

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

\(\frac{[x][x+3] - [x+2][x-2]}{[x-2][x+3]}\)

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

=  \(\frac{3x - 4}{[x-2][x+3]}\)