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

1 Answer
Mar 12, 2018

Answer:

#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))#.