How do you express 1(x+5)2(x−1) in partial fractions?

1 Answer
George C.
Sep 30, 2016

1(x+5)2(x−1)=−16(x+5)2−136(x+5)+136(x−1)

Explanation:

1(x+5)2(x−1)=A(x+5)2+Bx+5+Cx−1

Multiplying both sides of this equation by (x+5)2 we get:

1x−1=A+B(x+5)+C(x+5)2x−1

Now let x=−5 to find:

A=1(−5)−1=−16

Multiplying both sides of the first equation by (x−1) we get:

1(x+5)2=A(x−1)(x+5)2+B(x−1)x+5+C

Now let x=1 to find:

C=1((1)+5)2=136

Going back to the first equation and making a common denominator we find:

1(x+5)2(x−1)=A(x+5)2+Bx+5+Cx−1

1(x+5)2(x−1)=A(x−1)+B(x−1)(x+5)+C(x+5)2(x+5)2(x−1)

So equating the coefficients of x2 in the numerator, we find:

B=−C=−136

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