# How do you simplify #(4x^2)/(4x^2-9)#?

##### 2 Answers

This expression does not simplify.

#### Explanation:

Do not be tempted to cancel the

Perhaps factorising the denominator will help?

This expression does not simplify.

Another way of writing this which might be considered "simple" is to decompose this into partial fractions.

This gives the answer

#### Explanation:

(Note that for all intents and purposes,

The separation through partial fractions will look like this:

#(4x^2)/((2x+3)(2x-3)) = A/(2x+3) + B/(2x-3)#

#4x^2 = A(2x-3) + B(2x+3)#

Let

#4(3/2)^2 = A(2(3/2)-3) + B(2(3/2)+3)#

#4(9/4) = 0A+6B#

#9 = 6B#

#3/2 = B#

Let

#4(-3/2)^2 = A(2(-3/2)-3)+B(2(-3/2)+3)#

#4(9/4) = -6A + 0B#

#9 = -6A#

#-3/2 = A#

Therefore:

#(4x^2)/((2x+3)(2x-3)) = (-3/2)/(2x+3) + (3/2)/(2x-3)#

#3/(2(2x-3))-3/(2(2x+3))#

*Final Answer*