Simplify ((x^2+10x+24)/(3x^2+3x))÷(x+6)

$\frac{x^{2} + 10 x + 24}{3 x^{2} + 3 x} \div (x + 6)$

Rewrite the division as a fraction.

$\frac{\frac{x^{2} + 10 x + 24}{3 x^{2} + 3 x}}{x + 6}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{x^{2} + 10 x + 24}{3 x^{2} + 3 x} \cdot \frac{1}{x + 6}$

Factor $x^{2} + 10 x + 24$ 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 $24$ and whose sum is $10$ .

$4, 6$

Write the factored form using these integers.

$\frac{(x + 4) (x + 6)}{3 x^{2} + 3 x} \cdot \frac{1}{x + 6}$

Simplify terms.

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

Factor $3 x$ out of $3 x^{2}$ .

$\frac{(x + 4) (x + 6)}{3 x (x) + 3 x} \cdot \frac{1}{x + 6}$

Factor $3 x$ out of $3 x$ .

$\frac{(x + 4) (x + 6)}{3 x (x) + 3 x (1)} \cdot \frac{1}{x + 6}$

Factor $3 x$ out of $3 x (x) + 3 x (1)$ .

$\frac{(x + 4) (x + 6)}{3 x (x + 1)} \cdot \frac{1}{x + 6}$

Cancel the common factor of $x + 6$ .

Factor $x + 6$ out of $(x + 4) (x + 6)$ .

$\frac{(x + 6) (x + 4)}{3 x (x + 1)} \cdot \frac{1}{x + 6}$

Cancel the common factor.

$\frac{(x + 6) (x + 4)}{3 x (x + 1)} \cdot \frac{1}{x + 6}$

Rewrite the expression.

$\frac{x + 4}{3 x (x + 1)}$

Simplify ((x^2+10x+24)/(3x^2+3x))÷(x+6)

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