Question

Express the difference below in the simplest form $?$

$\frac{8}{x^2-4}-\frac{3}{x-2}$

Answer 1

Find the difference in the simplest form:

$\frac{8}{x^2-4}-\frac{3}{x-2}$$=\frac{8}{(x-2)(x+2)}-\frac{3}{x-2}\left[\because a^2-b^2=(a-b)(a+b)\right]$

$$\begin{gathered} =\frac{8-3(x+2)}{(x-2)(x+2)} \\ =\frac{8-3x-6}{(x-2)(x+2)}\left[\mathrm{Add}\mathrm{like}\mathrm{terms}\mathrm{together}\right] \end{gathered}$$

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

Hence, the difference in the simplest form is $\frac{\mathbf{-}\mathbf{3}\mathbf{x}\mathbf{+}\mathbf{2}}{\mathbf{(}\mathbf{x}\mathbf{-}\mathbf{2}\mathbf{)}\mathbf{(}\mathbf{x}\mathbf{+}\mathbf{2}\mathbf{)}}$.