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

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

Step 1

Factor $x^{2} + 3 x + 2$ 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 $3$ .

$1, 2$

Write the factored form using these integers.

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

Step 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 $- 1$ .

$- 2, 1$

Write the factored form using these integers.

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

Step 3

Cancel the common factor of $x + 1$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

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