# How do you simplify (x^2-3x-10)/(x^2-8x+15) * (x^2+5x-6)/(x^2+4x+4)?

May 26, 2015

Let's start by factoring all of the expressions:

$\frac{{x}^{2} - 3 x - 10}{{x}^{2} - 8 x + 15} \cdot \frac{{x}^{2} + 5 x - 6}{{x}^{2} + 4 x + 4}$

((x-5)(x+2))/((x-5)(x-3)) * ((x+6)(x-1))/((x+2)(x+2)

We can cancel out $\left(x - 5\right) \mathmr{and} \left(x + 2\right)$.

((x+6)(x-1))/((x-3)(x+2)

FOILing in back in gives us:

$\frac{{x}^{2} + 6 x - x - 6}{{x}^{2} - 3 x + 2 x - 6}$

$\frac{{x}^{2} + 5 x - 6}{{x}^{2} - x - 6}$