Question

Solve

$\frac{3x^2-x-2}{x^2-7x+12}÷\frac{3x^2-7x-6}{x^2-4}$

Answer 1

$\frac{3x^2-x-2}{x^2-7x+12}÷\frac{3x^2-7x-6}{x^2-4}$

$⟹\frac{3x^2-x-2}{x^2-7x+12}\times \frac{x^2-4}{3x^2-7x-6}$

$⟹\frac{3x^2-3x+2x-2}{x^2-3x-4x+12}\times \frac{(x-2)(x+2)}{3x^2-9x+2x-6}$

$⟹\frac{\left(3x\right(x-1)+2(x-1)}{x(x-3)-4(x-3)}\times \frac{(x-2)(x+2)}{3x(x-3)+2(x-3)}$

$⟹\frac{3x+2\left)\right(x-1)}{(x-4)(x-3)}\times \frac{(x-2)(x+2)}{(3x+2)(x-3)}$

$⟹\frac{(x-1)(x+2)(x-2)}{(x-3{)}^2(x-4)}$