# How do you multiply (x-7)/(x^2+9x+20)*(x+4)/(x^2-49)?

Mar 12, 2018

$\frac{1}{\left(x + 7\right) \left(x + 5\right)}$

#### Explanation:

Factorise the denominators first.
${x}^{2} + 9 x + 20$

The factors that multiply to $c$ $\left(20\right)$ and add to $b$ $\left(9\right)$ are $5$ and $4$.
Therefore ${x}^{2} + 9 x + 20 = \left(x + 5\right) \left(x + 4\right)$.

${x}^{2} - 49$ is a difference of two squares.
The formula for a difference of two squares is as follows:
${a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)$

Therefore ${x}^{2} - 49 = \left(x + 7\right) \left(x - 7\right)$.
Our new expression is (x-7)/((x+4)(x+5)) * (x+4)/((x+7)(x-7).
We can cancel similar brackets.

Our final expression is $\frac{1}{\left(x + 7\right) \left(x + 5\right)}$.