The partial fraction of x^2 x^2+3 x-4 is

Step-by-step solution

x^2 x^2+3 x-4 gathered = x^2 (x-1)(x+4) =1+ 4-3 x (x-1)(x+4) Let -3 x+4 (x-1)(x+4) = A x-1 + B x+4 -3 x+4 (x-1)(x+4) = A(x+4)+B(x-1) (x-1)(x+4) -3 x+4=x(A+B)+(4 A-B) gathered On compiaring the coefficients on both sides aligned & A+B=-3 and 4 A-B=4 & B=-3-A & 4 A-(-3-A)=4 & 5 A=1 & A=1 / 5 & B=-3- 1 5 = -16 5 & x^2 x^2+3 x-4 =1+ 1 5(x-1) + -16 5(x+4) & aligned