Engineering Board Exam Reviewer · Partial Fractions and Rational Expressions · hard

If x2+1/(x-1)2(x+2)=A/x-1+B/(x-1)2+C/x+2, find B.

1. 1/3
2. 2/3
3. 2
4. 4/9

Answer

B. 2/3

Solution

Multiply by (x-1)2 and set x=1: B=1+1/1+2= 23. (Also C=4+1/(-3)2= 59 and, comparing the x2 terms, A+C=1 A= 49.)

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