Question

How do you express `x/ (x^3-2x^2+x)` in partial fractions?

Answer 1

The answer is `=1/(x-1)^2`

Explanation:

We need

`(a-b)^2=a^2-2ab+b^2`

Let's factorise the denominator

`x^3-2x^2+x=x(x^2-2x+1)=x(x-1)^2`

So,

`x/(x^3-2x^2+x)=cancelx/(cancelx(x-1)^2)=1/(x-1)^2`

Fraction is already in irreductible form