Question

How do you combine `1/(x-1) - x/(x^2+1)`?

Answer 1

Use the common denominator `(x-1)(x^2+1)` and get:
`1/(x-1)-x/(x^2+1)=(x^2+1-x(x-1))/((x-1)(x^2+1))=`
`=(cancel(x^2)+1cancel(-x^2)+x)/((x-1)(x^2+1))=(x+1)/((x-1)(x^2+1))`