Simplify (x^2+12x+35)/(3x+15)

$\frac{x^{2} + 12 x + 35}{3 x + 15}$

Step 1

Factor $x^{2} + 12 x + 35$ 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 $35$ and whose sum is $12$ .

$5, 7$

Write the factored form using these integers.

$\frac{(x + 5) (x + 7)}{3 x + 15}$

Step 2

Simplify terms.

Factor $3$ out of $3 x + 15$ .

Factor $3$ out of $3 x$ .

$\frac{(x + 5) (x + 7)}{3 (x) + 15}$

Factor $3$ out of $15$ .

$\frac{(x + 5) (x + 7)}{3 x + 3 \cdot 5}$

Factor $3$ out of $3 x + 3 \cdot 5$ .

$\frac{(x + 5) (x + 7)}{3 (x + 5)}$

Cancel the common factor of $x + 5$ .

Cancel the common factor.

$\frac{(x + 5) (x + 7)}{3 (x + 5)}$

Rewrite the expression.

$\frac{x + 7}{3}$

Simplify (x^2+12x+35)/(3x+15)

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