Suggest You - Reducing a Simple Algebraic Fraction

First, let me explain the syntax we will be using. All algebraic expressions will be written in 'one-line' notation, using common calculator operations(+,-,*,/ and ^). The only one that you might not be familiar with, could be '^' which stands for exponentiation (i.e. x^2 means "x squared"). In addition, when radicals are needed, "R" will be used (i.e. 3R(x^2) would stand for "cube root of x squared"). This syntax is a little cumbersome; however you can cut and paste any of these expressions to a 'syntax converter' located at this algebra resources Ultrasound Vocational Schools
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So, here is the problem:

(4*x^2-9*y^2)/(2*x+3*y)^2

The first thing that has to be done is completely factor both numerator and the denominator. Since denominator is already factored, let's concentrate on the numerator. If you look at it closely, you will realize that it represents a difference of two squares. We first need to make this difference explicit (more obvious):

((2*x)^2-(3*y)^2)/(2*x+3*y)^2

Now it is a little clearer that we can use the following 'difference o

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