Answer
$2x/(2-x)$
Work Step by Step
$\frac{x^{-1}+2^{-1}}{x^{-2}-4^{-1}}$
$\frac{\frac{1}{x}+\frac{1}{2}}{\frac{1}{x^2}-\frac{1}{4}}$
LCD of $x, 2, x^2, 4$ is 4x^2
$\frac{\frac{1}{x}+\frac{1}{2}}{\frac{1}{x^2}-\frac{1}{4}}$
$(4x^2)\frac{\frac{1}{x}+\frac{1}{2}}{\frac{1}{x^2}-\frac{1}{4}}$
$\frac{\frac{4x^2}{x}+\frac{4x^2}{2}}{\frac{4x^2}{x^2}-\frac{4x^2}{4}}$
$(4x+2x^2)/(4-x^2)$
$2x(2+x)/(2-x)(2+x)$
$2x/(2-x)$
