Answer:
-1
Step-by-step explanation:
(4x − 1) / ((x + 1) (2x − 3)) = A / (x + 1) + B / (2x − 3)
Combine the right hand side into one fraction by finding the common denominator.
(A (2x − 3) + B (x + 1)) / ((x + 1) (2x − 3))
(2Ax − 3A + Bx + B) / ((x + 1) (2x − 3))
((2A + B)x + B − 3A) / ((x + 1) (2x − 3))
Set the numerator of this fraction equal to the numerator of the original fraction.
4x − 1 = (2A + B)x + B − 3A
Match the coefficients.
4 = 2A + B
-1 = B − 3A
Solve the system of equations. Subtracting the second equation from the first:
5 = 5A
A = 1
B = 2
A − B = -1
