Question

Simply the expression given below. x^2+x-2/x^3-x^2+2x-2

Answer 1

Explanation:

(x-1)(x+2)/x^2(x-1)+2(x-1)

(x-1)(x+2)/(x-1)(x^2+2)

(x+2)/(x^2+2)

Answer 2

`((x+2))/((x^2+2))`

Explanation:

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

To simplify the given expression , factor both numerator and denominator

Numerator :
`x^2+x-2`

Product is -2 and sum is +1. factors are 2 and -1

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

Denominator :
`x^3-x^2+2x-2`

Group first two terms and last two terms

Factor out GCF from each term

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

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

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

Replace the factors in the given expression

`((x+2)(x-1))/((x^2+2)(x-1))`

Cancel out x-1 at the top and bottom

`((x+2))/((x^2+2))`