Question

Find the values of x. which satisfy the inequality $\frac{x-2}{x+2}>\frac{2x-3}{4x-1}.$

Answer 1

$\frac{x-2}{x+2}-\frac{2x-3}{4x-1}>0$

$\Rightarrow \frac{2(x^2-5x+4)}{(x+2)(4x-1)}>0$
$\Rightarrow \frac{2(x-4)(x-1)}{(x+2)(4x-1)}>0$ $\Rightarrow \frac{2(x-4)(x-1)}{4(x-2)(x-\frac{1}{4})}>0$
$\Rightarrow x>-2$ or $\frac{1}{4}<x<1$ or $x>4$