Answer
$\frac{5x-6}{x(x-1)}$
Work Step by Step
$\frac{2}{x}+\frac{3}{x-1}-\frac{4}{x^{2}-x}$
Factor the expression $x^{2}-x$ and replace in denominator:
$=\frac{2}{x}+\frac{3}{x-1}-\frac{4}{x(x-1)}$
Find the lowest common denominator (i.e. $x(x-1)$) and adjust the fractions accordingly:
$=\frac{2\times (x-1)}{x\times (x-1)}+\frac{3\times x}{(x-1) \times x}-\frac{4}{x(x-1)}$
$=\frac{2(x-1)}{x(x-1)}+\frac{3x}{x(x-1)}-\frac{4}{x(x-1)}$
Combine the fractions:
$=\frac{2(x-1)+3x-4}{x(x-1)}$
Expand any brackets in the numerator:
$=\frac{2x-2+3x-4}{x(x-1)}$
Simplify:
$=\frac{5x-6}{x(x-1)}$
