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

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

Factor $x^{2} + x - 2$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 2$ and whose sum is $1$ .

$- 1, 2$

Write the factored form using these integers.

$\frac{(x - 1) (x + 2)}{x^{3} - x^{2} + 2 x - 2}$

Simplify the denominator.

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{(x - 1) (x + 2)}{(x^{3} - x^{2}) + 2 x - 2}$

Factor out the greatest common factor (GCF) from each group.

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

Factor the polynomial by factoring out the greatest common factor, $x - 1$ .

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

Cancel the common factor of $x - 1$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

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