Simplify (xy-2x+3y-6)/(x^2+8x+15)

$\frac{x y - 2 x + 3 y - 6}{x^{2} + 8 x + 15}$

Simplify the numerator.

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{(x y - 2 x) + 3 y - 6}{x^{2} + 8 x + 15}$

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

$\frac{x (y - 2) + 3 (y - 2)}{x^{2} + 8 x + 15}$

Factor the polynomial by factoring out the greatest common factor, $y - 2$ .

$\frac{(y - 2) (x + 3)}{x^{2} + 8 x + 15}$

Factor $x^{2} + 8 x + 15$ 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 $15$ and whose sum is $8$ .

$3, 5$

Write the factored form using these integers.

$\frac{(y - 2) (x + 3)}{(x + 3) (x + 5)}$

Cancel the common factor of $x + 3$ .

Cancel the common factor.

$\frac{(y - 2) (x + 3)}{(x + 3) (x + 5)}$

Rewrite the expression.

$\frac{y - 2}{x + 5}$

Simplify (xy-2x+3y-6)/(x^2+8x+15)

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