Simplify ((3x+6)/(x+3))÷((x+3)/(2x))*((x+3)^2)/6

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

Step 1

Combine.

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

Step 2

Factor $3$ out of $3 x + 6$ .

Factor $3$ out of $3 x$ .

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

Factor $3$ out of $6$ .

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

Factor $3$ out of $3 x + 3 \cdot 2$ .

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

Step 3

Combine $\frac{3 (x + 2)}{x + 3}$ and ${(x + 3)}^{2}$ .

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

Step 4

Combine $\frac{x + 3}{2 x}$ and $6$ .

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

Step 5

Reduce the expression by cancelling the common factors.

Reduce the expression $\frac{3 (x + 2) {(x + 3)}^{2}}{x + 3}$ by cancelling the common factors.

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

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

Multiply by $1$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $3 (x + 2) (x + 3)$ by $1$ .

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

Step 6

Simplify the denominator.

Reduce the expression $\frac{(x + 3) \cdot 6}{2 x}$ by cancelling the common factors.

Factor $2$ out of $(x + 3) \cdot 6$ .

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

Factor $2$ out of $2 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move $3$ to the left of $x + 3$ .

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

Step 7

Multiply the numerator by the reciprocal of the denominator.

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

Step 8

Cancel the common factor of $3 (x + 3)$ .

Factor $3 (x + 3)$ out of $3 (x + 2) (x + 3)$ .

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

Cancel the common factor.

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

Rewrite the expression.

$(x + 2) x$

Step 9

Apply the distributive property.

$x \cdot x + 2 x$

Step 10

Multiply $x$ by $x$ .

$x^{2} + 2 x$

Simplify ((3x+6)/(x+3))÷((x+3)/(2x))*((x+3)^2)/6

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