Find the partial fraction decomposition 146x2x2Solution146x2

Find the partial fraction decomposition. (-14)/(6x^2--x--2)

Solution

(-14)/(6x^2-x-2) = -14/(6x^2 -4x +3x -2)

=-14/(2x(3x- 2)+1(3x-2))

= -14/(2x+1)(3x-2)

Let  -14/(2x+1)(3x-2) = A/(2x+1) +B/(3x-2)

= A(3x) -2A +B(2x) +B

-14/(2x+1)(3x-2) = x(3A +2B) +B -2A

B- 2A = -14 ----(1)

3A + 2B =0 ---(2)

B = -14+2A

3A +2(-14 +2A) =0---> -A -28 =0

A = -28

B = -14 +2(-28) = -70

-14/(2x+1)(3x-2) = -28/(2x+1) -70/(3x-2)