How do you simplify and restricted value of (x^2-36)/(3x+6) ?

Jul 18, 2017

$\frac{\left(x - 6\right) \left(x + 6\right)}{3 \left(x + 2\right)}$; $x \ne - 2$

Explanation:

Given: $\frac{{x}^{2} - 36}{3 x + 6}$

The numerator is the difference of squares $\left({a}^{2} - {b}^{2}\right) = \left(a - b\right) \left(a + b\right) : \left({x}^{2} - {6}^{2}\right) = \left(x - 6\right) \left(x + 6\right)$

Rewriting the given expression yields: $\frac{\left(x - 6\right) \left(x + 6\right)}{3 x + 6}$

The denominator can be factored using the greatest common factor (GCF) of $3 : 3 \left(x + 2\right)$

Rewriting the given expression yields: $\frac{\left(x - 6\right) \left(x + 6\right)}{3 \left(x + 2\right)}$

Since there is a fraction, the denominator cannot be $= 0$. This means that $3 \left(x + 2\right) \ne 0$, or $x + 2 \ne 0$. This occurs when $x = - 2$.