Simplify (x+2)/(x-1)*(x^2-x-2)/(x^2-x-6)

$\frac{x + 2}{x - 1} \cdot \frac{x^{2} - x - 2}{x^{2} - x - 6}$

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 $- 1$ .

$- 2, 1$

Write the factored form using these integers.

$\frac{x + 2}{x - 1} \cdot \frac{(x - 2) (x + 1)}{x^{2} - x - 6}$

Factor $x^{2} - x - 6$ 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 $- 6$ and whose sum is $- 1$ .

$- 3, 2$

Write the factored form using these integers.

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

Simplify terms.

Cancel the common factor of $x + 2$ .

Factor $x + 2$ out of $(x - 3) (x + 2)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $\frac{1}{x - 1}$ by $\frac{(x - 2) (x + 1)}{x - 3}$ .

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

Simplify (x+2)/(x-1)*(x^2-x-2)/(x^2-x-6)

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