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Lucas
07-12-2013, 05:11 PM
SAT math question about Factoring

How can I factor the following expression:

\frac{(a-2)^2-4}{a-4}+\frac{(a+1)^2-1}{a+2}


Thanks!!

elizabeth
07-12-2013, 05:18 PM
SAT maths question about Factoring

Factoring or Factorising is the process of finding the factors of an expression.
The following expression is called a difference of two squares
x^2-y^2=(x-y)(x+y)

So using the identity of the difference of two squares, we have:

\frac{(a-2)^2-4}{a-4}+\frac{(a+1)^2-1}{a+2}=

\frac{(a-2)^2-2^2}{a-4}+\frac{(a+1)^2-1^2}{a+2}=

\frac{((a-2)-2)((a-2)+2)}{a-4}+\frac{((a+1)-1)((a+1)+1)}{a+2}=

\frac{a(a-4)}{a-4}+\frac{a(a+2)}{a+2}=2a

Hope these help!!:D:D

Lucas
07-12-2013, 05:18 PM
Thanks Elisabeth!!