SOLUTION: (x)/(x^2+9x+20) - (4)/(x^2+7x+12) I am having trouble with this problem. Thanks for any help Rhee

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: (x)/(x^2+9x+20) - (4)/(x^2+7x+12) I am having trouble with this problem. Thanks for any help Rhee      Log On


   

Question 110103: (x)/(x^2+9x+20) - (4)/(x^2+7x+12) I am having trouble with this problem.
Thanks for any help
Rhee
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%29%2F%28x%5E2%2B9x%2B20%29+-+%284%29%2F%28x%5E2%2B7x%2B12%29

First factor this: %28x%5E2%2B9x%2B20%29 and %28x%5E2%2B7x%2B12%29

%28x%5E2%2B9x%2B20%29

%28x%5E2%2B4x+%2B+5x+%2B20%29 Group the first two terms together and the last two terms together

%28%28x%5E2%2B4x%29+%2B+%285x+%2B20%29%29

%28x%28x%2B4%29+%2B+5%28x+%2B+4%29%29

%28x%2B4%29+%28x+%2B+5%29


%28x%5E2%2B7x%2B12%29

%28x%5E2%2B3x+%2B+4x+%2B+12%29 Group the first two terms together and the last two terms together

%28%28x%5E2%2B3x%29+%2B+%284x+%2B+12%29%29

%28x%28x%2B3%29+%2B+4%28x+%2B+3%29%29

%28x%2B3%29+%28x+%2B+4%29

Then we will have:

x%2F%28x%2B4%29%28x+%2B+5%29 – 4%2F%28x%2B3%29%28x+%2B+4%29%29………common denominator is %28x%2B4%29%28x%2B5%29%28x%2B3%29

(x%28x%2B3%29–4%28x%2B5%29)/%28x%2B3%29%28x+%2B+4%29%28x%2B5%29………

%28x%5E2%2B3x+-4x+%2B+20%29%2F%28x%2B3%29%28x+%2B+4%29%28x%2B5%29

%28x%5E2+-x+%2B+20%29%2F%28x%2B3%29%28x+%2B+4%29%28x%2B5%29

since %28x%5E2+-x+%2B+20%29 cannot be factored, final result is:

%28x%5E2+-x+%2B+20%29%2F%28x%2B3%29%28x+%2B+4%29%28x%2B5%29