Question

What is the solution to the equation StartFraction negative 3 d Over d squared minus 2 d minus 8 EndFraction + StartFraction 3 Over d minus 4 EndFraction = StartFraction negative 2 Over d + 2 EndFraction?
d = –4 and d = 2
d = –2 and d = 4
d = 1
d = 2

Answer 1

Factor denominator: d^2 − 2d − 8 = (d − 4)(d + 2). Multiply both sides by (d − 4)(d + 2) (with d ≠ 4, −2):

-3d + 3(d + 2) = -2(d − 4)
-3d + 3d + 6 = -2d + 8
6 = -2d + 8 → -2 = -2d → d = 1

d = 1 (note d ≠ 4, −2).