SOLUTION: Can someone help me to solve this? How to write the fraction -2x+34/x^2-2x-15 as the sum of two fractions with different denominators? Thank you.

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: Can someone help me to solve this? How to write the fraction -2x+34/x^2-2x-15 as the sum of two fractions with different denominators? Thank you.       Log On


   

Question 1074146: Can someone help me to solve this?
How to write the fraction -2x+34/x^2-2x-15 as the sum of two fractions with different denominators?
Thank you.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
(Partial Fraction Decomposition)

%28-2x%2B34%29%2F%28%28x%2B3%29%28x-5%29%29

A%2F%28x%2B3%29%2BB%2F%28x-5%29

Those must be equal.

%28-2x%2B34%29%2F%28%28x%2B3%29%28x-5%29%29=A%2F%28x%2B3%29%2BB%2F%28x-5%29

Multiply the left member and the right member by simplest common denominator of %28x%2B3%29%28x-5%29.

-2x%2B34=A%28x-5%29%2BB%28x%2B3%29

-2x%2B34=Ax-5A%2BBx%2B3B
-2x%2B34=Ax%2BBx%2B3B-5A
-2x%2B34=%28A%2BB%29x%2B%283B-5A%29

Compare corresponding coefficients.
system%28A%2BB=-2%2C-5A%2B3B=34%29-------Solve this system.
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Finish forming the sum began above.