Answer
$\frac{x(x-1)}{(x+5)(x-2)(x+3)}; x \ne -5,2,-3;$
Work Step by Step
$\frac{3x}{x^{2}+3x-10} - \frac{2x}{x^{2}+x-6} $
Factorizing the denominator,
$=\frac{3x}{(x+5)(x-2)} - \frac{2x}{(x+3)(x-2)}; x \ne -5,2,-3;$
Taking Least Common Denominator, we get
$=\frac{3x(x+3)-2x(x+5)}{(x+5)(x-2)(x+3)}; x \ne -5,2,-3;$
$=\frac{3x^{2}+9x-2x^{2}-10x}{(x+5)(x-2)(x+3)}; x \ne -5,2,-3;$
Combine like terms.
$=\frac{x^{2}-x}{(x+5)(x-2)(x+3)}; x \ne -5,2,-3;$
$=\frac{x(x-1)}{(x+5)(x-2)(x+3)}; x \ne -5,2,-3;$
