SOLUTION: Find the values of a and b that make the following expression an identity: (5x)/((x−2)(x+3)) = a/(x−2) + b/(x+3)

Algebra ->  Finance -> SOLUTION: Find the values of a and b that make the following expression an identity: (5x)/((x−2)(x+3)) = a/(x−2) + b/(x+3)       Log On


   



Question 1140272: Find the values of a and b that make the following expression an identity:
(5x)/((x−2)(x+3)) = a/(x−2) + b/(x+3)

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


(1) multiply both sides of the equation by the least common denominator, (x-2)(x+3)

5x+=+a%28x%2B3%29%2Bb%28x-2%29
5x+=+ax%2B3a%2Bbx-2b
5x+%2B+0+=+%28a%2Bb%29x+%2B+%283a-2b%29

The coefficient of x must be the same on both sides; and the constant must be the same on both sides. This gives you a system of two equations in a and b that you can solve to find the solution to the problem.

a%2Bb+=+5
3a-2b+=+0

Solve by any of a number of basic methods.