SOLUTION: Find the values of a and b that make the following expression an identity: (5x+31)/((x−5)(x+2)) = a/(x−5) − b/(x+2)

Question 1140273: Find the values of a and b that make the following expression an identity:
(5x+31)/((x−5)(x+2)) = a/(x−5) − b/(x+2)
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Multiply everything by (x-5)(x+2)
the left side is 5x+31
the right side is a(x+2)-b(x-5)
so ax+2a-bx+5b=5x+31
x(a-b)+2a+5b=5x+31; set the x term=5 and the constant term=31
a-b=5
2a+5b=31
5a-5b=25
so 7a=56, a=8
b=3
(8, 3)
check with x=7
66/(18)=(8/2)-3/9=3 2/3 checks

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