Resolve (frac{3x – 1}{(x – 2)^{2}}, x neq 2) into partial fractions.
-
A.
(frac{x}{2(x – 2)} – frac{5}{(x – 2)^{2}}) -
B.
(frac{5}{(x – 2)} + frac{x}{2(x – 2)^{2}}) -
C.
(frac{1}{2(x – 2)} + frac{5x}{2(x- 2)^{2}}) -
D.
(frac{-1}{2(x – 2)} + frac{8x}{2(x – 2)^{2}})
Correct Answer: Option C
Explanation
(frac{3x – 1}{(x – 2)^{2}} = frac{A}{(x – 2)} + frac{Bx}{(x – 2)^{2}})
(frac{3x – 1}{(x – 2)^{2}} = frac{A(x – 2) + Bx}{(x – 2)^{2}})
Comparing, we have
(3x – 1 = Ax – 2A + Bx implies -2A = -1; A + B = 3)
(therefore A = frac{1}{2}; B = frac{5}{2})
= (frac{1}{2(x – 2)} + frac{5x}{2(x – 2)^{2}})