Question

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

Answer 1

`1/((x+7)(x+5))`

Explanation:

Factorise the denominators first.
`x^2 + 9x + 20`

The factors that multiply to `c` `(20)` and add to `b` `(9)` are `5` and `4`.
Therefore `x^2 + 9x + 20 = (x+5)(x+4)`.

`x^2 - 49` is a difference of two squares.
The formula for a difference of two squares is as follows:
`a^2 - b^2 = (a+b)(a-b)`

Therefore `x^2 - 49 = (x+7)(x-7)`.
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 `1/((x+7)(x+5))`.