# How do you simplify  [(x^2 - 2x - 15) / [(x - 6)(x - 3)]] * [(x^2 - 6) / (x - 5)]?

Jul 18, 2017

Factorise, multiply then simplify.

#### Explanation:

1. Factorise all statements that can be factorised.
${x}^{2} - 2 x - 15 = \left(x + 3\right) \left(x - 5\right)$
${x}^{2} - 6 = \left(x + \sqrt{6}\right) \left(x - \sqrt{6}\right)$

2. Then multiply the two brackets. Remember to multiply fractions multiply the numerators by each other and repeat with denominators.
$\frac{\left(x + 3\right) \left(x - 5\right) \left(x + \sqrt{6}\right) \left(x - \sqrt{6}\right)}{\left(x - 6\right) \left(x - 3\right) \left(x - 5\right)}$

3. Simplify by removing like terms in the numerator and denominator.
$\frac{\left(x + 3\right) \left(x + \sqrt{6}\right) \left(x - \sqrt{6}\right)}{\left(x - 6\right) \left(x - 3\right)}$

I know it looks complicated but it is fully simplified, hope this has helped.