How do you express x1x3+x2 in partial fractions?

1 Answer
Oct 29, 2016

The answer is x1x3+x2=2x1x22x+1

Explanation:

Some factorisation to start with
x1x3+x2=x1(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
x1=Ax(x+1)+B(x+1)+Cx2
let x=-1, 2=CC=2
Coefficients of x2, 0=A+CA=2
Coefficients of x, 1=A+BB=1

And finally, we have
x1x3+x2=2x1x22x+1