Simplify (2x+9)/(x^2+5x+6)-(x+7)/(x^2+5x+6)

$\frac{2 x + 9}{x^{2} + 5 x + 6} - \frac{x + 7}{x^{2} + 5 x + 6}$

Simplify terms.

Combine the numerators over the common denominator.

$\frac{2 x + 9 - (x + 7)}{x^{2} + 5 x + 6}$

Simplify each term.

Apply the distributive property.

$\frac{2 x + 9 - x - 1 \cdot 7}{x^{2} + 5 x + 6}$

Multiply $- 1$ by $7$ .

$\frac{2 x + 9 - x - 7}{x^{2} + 5 x + 6}$

Simplify by adding terms.

Subtract $x$ from $2 x$ .

$\frac{x + 9 - 7}{x^{2} + 5 x + 6}$

Subtract $7$ from $9$ .

$\frac{x + 2}{x^{2} + 5 x + 6}$

Factor $x^{2} + 5 x + 6$ 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 $5$ .

$2, 3$

Write the factored form using these integers.

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

Cancel the common factor of $x + 2$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{x + 3}$

Simplify (2x+9)/(x^2+5x+6)-(x+7)/(x^2+5x+6)

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