Problem: The fraction 2x2+x−65x−11 was obtained by adding the two fractions x+2A and 2x−3B. The values of A and B must be:
Answer Choices:
A. A=5x, B=−11
B. A=−11, B=5x
C. A=−1, B=3
D. A=3, B=−1
E. A=5, B=−11
Solution:
(x+2)(2x−3)A(2x−3)+B(x+2)=2x2+x−65x−11;
A(2x−3)+B(x+2)≡5x−11.
Equating the coefficients of like powers of x, we obtain 2A+B=5,
−3A+2B=−11;∴A=3,B=−1.