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

1 Answer
Mar 12, 2018

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)).