Find values of a and b that make the following equality into identity:
x−1/(x+1)(x−4) = a/x+1 + b/x−4

The value of a and b in given expression must be respectively so that given equality becomes identity.

Need to find the value of a and b in following expression so that following equality will become identity.

  ------- eqn 1

Lets Simplify Right hand Side first,

On multiplying both sides by (x+1)(x-4) we get

On comparing coefficient of x and constant term separately, we get

a + b = 1 and 4a - b = 1

On adding the two equations we get

a + b + 4a - b = 1 + 1

=> 5a = 2

=>

So the value of a and b in given expression must be so that given equality becomes identity.