Question

reslove into partial fraction​

Answer 1

Some factorisation to start with

x−1x3+x2=x−1(x2)(x+1)

=Ax+Bx2+Cx+1

=Ax(x+1)+B(x+1)+Cx2(x2)(x+1)

So now we can solve for A,B,andC

x−1=Ax(x+1)+B(x+1)+Cx2

let x=-1, −2=C⇒C=−2

Coefficients of x2, 0=A+C⇒A=2

Coefficients of x, 1=A+B⇒B=−1

And finally, we have

x−1x3+x2=