SOLUTION: 5x/x^2-x-6 - 4/x^2+4x+4 How do you factor this problem out step by step?

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Question 64574This question is from textbook PRENTICE HALL MATHMATICS ALGEBRA 2
: 5x/x^2-x-6 - 4/x^2+4x+4
How do you factor this problem out step by step? This question is from textbook PRENTICE HALL MATHMATICS ALGEBRA 2

Found 2 solutions by 303795, FadelSalem:
Answer by 303795(602) About Me  (Show Source):
You can put this solution on YOUR website!
5x%2F%28x%5E2-x-6%29++-++4%2F%28x%5E2%2B4x%2B4%29
Factorise the expressions on the bottom of the fractions.
5x%2F%28x-3%29%28x%2B2%29++-++4%2F%28%28x%2B2%29%28x%2B2%29%29
The common factor on the bottom will be (x-3)(x+2)(x+2). Multiply the first term by (x+2)/(x+2). Multiply the second term by (x-3)/(x-3). This will rewrite both terms so they are over the common denominator.

Multiply out the top parts of the problem

Rewrite over the common denominator
%285x2%2B10x+-%284x-12%29%29%2F%28%28x-3%29%28x%2B2%29%28x%2B2%29%29
%285x2%2B10x+-+4x%2B12%29%2F%28%28x-3%29%28x%2B2%29%28x%2B2%29%29
%285x2%2B6x%2B12%29%2F%28%28x-3%29%28x%2B2%29%28x%2B2%29%29

Answer by FadelSalem(12) About Me  (Show Source):
You can put this solution on YOUR website!
5x/x^2-x-6 - 4/x^2+4x+4 =
5x/(x-3)(x+2) - 4/(x+2)^2 =
5x(x+2)/(x-3)(x+2)^2 - 4(x-3)/(x-3)(x+2)^2 =
(5x^2+10x)/(x-3)(x+2)^2 + (-4x + 12)/(x-3)(x+2)^2 =
(5x^2 + 6x + 12)/(x-3)(x+2)^2
Happy New Year
Fadel Salem
Egypt
fadelsalem@hotmail.com