Express the following in partial fraction and hence differentiate

Question

Y=3x_1/(x+2)(2x_1)

Answer 1

(3x-1)/((x+2)(2x-1)) = A/(x+2) + B/(2x-1)
3x-1 = A(2x-1) + B(x+2)
so
2A+B = 3
-A+2B = -1
solve for A and B

Answer 2

or, once you get to oobleck's 3x-1 = A(2x-1) + B(x+2)
let x = -2 ----> -7 = -5A + 0 , A = 7/5
let x = 1/2 ---> 1/2 = 0 + 5/2 B, B = 1/5