# Math33333

Problem:
x+2 x-3
_________ - _________
2x^2+5x+2 2x^2-5x-3
*Simplify the expression

2x^2+5x+2 =(x+2)(2x+1)
2x^2-5x-3 =(2x+1)(x-3)
So x+2/(x+2)(2x+1) = 1/2x+1
x-3/(2x+1)(x-3) = 1/2x+1
Finally 1/2x+1 - 1/2x+1 = 0

Let's take a look at the problem:

(x+2)/(2x^2+5x+2) - (x-3)/(2x^2-5x-3)

Let's try to factor the denominators first:

2x^2+5x+2 factors are (2x+1)(x+2)
2x^2-5x-3 factors are (2x+1)(x-3)

Now, let's rewrite the problem:

(x+2)/(2x+1)(x+2) - (x-3)/(2x+1)x-3)

Reduce each fraction, then you will have the same denominator for both fractions. Once you do those steps, you should easily see what the answer will be.

I hope this helps.

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