# How do you simplify (2-p)/(p^2-p-2)?

Sep 3, 2016

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

#### Explanation:

Well you have to do something so factorise the denominator
$\frac{2 - p}{\left(p - 2\right) \left(p + 1\right)}$

And it helps
$- \frac{\left(p - 2\right)}{\left(p - 2\right) \left(p + 1\right)}$

Cancel
-1/(p+1

Sep 3, 2016

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

#### Explanation:

The first step is to factorise the denominator.

$\Rightarrow {p}^{2} - p - 2$

Consider the factors of - 2 which sum to give the coefficient of the middle term, that is - 1.

These are - 2 and + 1 , since.

$\left(- 2 \times + 1\right) = - 2 \text{ and } - 2 + 1 = - 1$

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

Fraction can now be expressed as $\frac{2 - p}{\left(p - 2\right) \left(p + 1\right)}$

Take out a common factor of - 1 in the numerator.

$\Rightarrow 2 - p = - 1 \left(p - 2\right)$

and now we have a fraction which may be simplified.

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