# How do you simplify the rational expression and state any restrictions on the variable (b^2 +6b-16)/(b+8)?

Apr 8, 2015

Extract a factor equal to the denominator from the numerator (note this is not always possible in every case, but it works in this example) and simplify.

Remember that, as a restriction, division by $0$ is invalid.

$\frac{{b}^{2} + 6 b - 16}{b + 8}$

$= \frac{\left(b - 2\right) \cancel{b + 8}}{\cancel{b + 8}}$ provided $b + 8 \ne 0$

$\frac{{b}^{2} + 6 b - 16}{b + 8} = b - 2$

provide $b \ne \left(- 8\right)$

Apr 8, 2015

The answer is $\left(b - 2\right)$.

Beginning Equation:

$\frac{{b}^{2} + 6 b - 16}{b + 8}$

Factor the numerator.

$\frac{\left(b - 2\right) \left(b + 8\right)}{b + 8}$

Cancel (b+8) from the numerator and denominator.

$\frac{\left(b - 2\right) \cancel{b + 8}}{\cancel{b + 8}}$

That leaves $\left(b - 2\right)$.