Question

How do you combine `(x^2 ) / (x^2 + x- 6) - 6 / ((x+3)(x-2)) + x / (x^2 + x - 6)`?

Answer 1

`(x^2 ) / (x^2 + x- 6) - 6 / ((x+3)(x-2)) + x / (x^2 + x - 6)`

The denominator of the second term upon expansion becomes
`(x+3)(x-2) = x^2 - 2x+3x -6 =x^2 + x- 6`

rewriting the expression:
`(x^2 ) / (x^2 + x- 6) - 6 / (x^2 + x- 6) + x / (x^2 + x - 6)`

since all terms have a common denominator the expression now becomes :
`(x^2 - 6 + x) / (x^2 + x - 6)`

rearranging the terms present in the numerator:

`cancel(x^2 + x -6) /cancel (x^2 + x - 6) = 1`