# How do you simplify and state the restrictions for (p^2-3p-10)/(p^2+p-2)?

Jun 6, 2018

$\frac{- {p}^{2} - 3 p - 10}{\left(p + 2\right) \cdot \left(p - 1\right)}$

#### Explanation:

Using that ${p}^{2} + p - 2 = \left(p + 2\right) \left(p - 1\right)$ we get the result above.

Jun 6, 2018

$\frac{p - 5}{p - 1}$

#### Explanation:

$\text{factorise numerator/denominator abd cancel any }$
$\text{common factors}$

$\textcolor{b l u e}{\text{numerator}}$

$\text{the factors of - 10 which sum to - 3 are - 5 and + 2}$

${p}^{2} - 3 p - 10 = \left(p - 5\right) \left(p + 2\right)$

$\textcolor{b l u e}{\text{denominator}}$

$\text{the factors of - 2 which sum to + 1 are + 2 and - 1}$

${p}^{2} + p - 2 = \left(p + 2\right) \left(p - 1\right)$

$\frac{{p}^{2} - 3 p - 10}{{p}^{2} + p - 2}$

$= \frac{\left(p - 5\right) \cancel{\left(p + 2\right)}}{\cancel{\left(p + 2\right)} \left(p - 1\right)} = \frac{p - 5}{p - 1}$

$\text{the denominator cannot equal zero as this would make}$
$\text{the fraction undefined}$

$p - 1 \ne 0 \Rightarrow p \ne 1$