Question

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

Answer 1

Answer:

Step-by-step 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

Answer:

$\frac{(x+2)}{(x^2+2)}$

Step-by-step explanation:

$\frac{x^2+x-2}{x^3-x^2+2x-2}$

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

$\frac{(x+2)(x-1)}{(x^2+2)(x-1)}$

Cancel out x-1 at the top and bottom

$\frac{(x+2)}{(x^2+2)}$