Answer:
-8
Step-by-step explanation:
f(x) = (4x − 2) / (x (x + 1))
Write f(x) as the sum of two fractions.
f(x) = A / x + B / (x + 1)
Combine back into one fraction using the least common denominator.
f(x) = (A (x + 1) + Bx) / (x (x + 1))
f(x) = ((A + B) x + A) / (x (x + 1))
This equals the original numerator of 4x − 2, so match the coefficients.
A + B = 4
A = -2
Solving for B, B = 6.
Therefore, A − B = -2 − 6 = -8.
