Answer
$\frac{x^{2}-6x-4}{(x-1)(x+2)(x-4)}$
Work Step by Step
$\frac{x}{x^{2}+x-2}-\frac{2}{x^{2}-5x+4}$
Factor the denominators:
$=\frac{x}{(x-1)(x+2)}-\frac{2}{(x-1)(x-4)}$
Find the lowest common denominator (i.e. $(x-1)(x+2)(x-4)$) and adjust the fractions accordingly:
$=\frac{x\times (x-4)}{(x-1)(x+2)(x-4)}-\frac{2\times (x+2)}{(x-1)(x+2)(x-4)}$
$=\frac{x^{2}-4x}{(x-1)(x+2)(x-4)}-\frac{2x+4}{(x-1)(x+2)(x-4)}$
Combine the fractions:
$=\frac{x^{2}-4x-2x-4}{(x-1)(x+2)(x-4)}$
Simplify:
$=\frac{x^{2}-6x-4}{(x-1)(x+2)(x-4)}$
