Question

Find A and B so that: ((1/(x-2)(x+3))=((A/(x-2))+ (B/(x+3))

Answer 1

basic partial fractions

Answer 2

multiply both sides by the denominator of the the LHS

so you get 1 = A(x+3) + B ( x-2)

Answer 3

now sub in brackets which makes the brackets zero

sub x=-3 --> 1 = -5B --> B= -1/5

sub x=2 --> 1 = 5A --> A= 1/5

A=1/5,

B=-1/5