Question

write the partial fraction decomposition of the rational expression

ax over x squared -x-2

or ax
____________
xsquared-x-2

Answer 1

let
ax/((x-2)(x+1)) = A/(x-2) + B/(x+1)

ax/((x-2)(x+1)) = (A(x+1) + B(x-2))/((x-2)(x+1))

ax = A(x+1) + B(x-2)

let x=2
2a = 3A ---- A = 2a/3

let x=-1
-a = -3B --- B = a/3

take it from there