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)

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) (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)

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.

Solve by any of a number of basic methods.
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