Simplify (x+7)/(5x^3)*(15x^2)/(2x+14)

$\frac{x + 7}{5 x^{3}} \cdot \frac{15 x^{2}}{2 x + 14}$

Step 1

Factor $2$ out of $2 x + 14$ .

Factor $2$ out of $2 x$ .

$\frac{x + 7}{5 x^{3}} \cdot \frac{15 x^{2}}{2 (x) + 14}$

Factor $2$ out of $14$ .

$\frac{x + 7}{5 x^{3}} \cdot \frac{15 x^{2}}{2 x + 2 \cdot 7}$

Factor $2$ out of $2 x + 2 \cdot 7$ .

$\frac{x + 7}{5 x^{3}} \cdot \frac{15 x^{2}}{2 (x + 7)}$

Step 2

Cancel the common factor of $x + 7$ .

Factor $x + 7$ out of $2 (x + 7)$ .

$\frac{x + 7}{5 x^{3}} \cdot \frac{15 x^{2}}{(x + 7) \cdot 2}$

Cancel the common factor.

$\frac{x + 7}{5 x^{3}} \cdot \frac{15 x^{2}}{(x + 7) \cdot 2}$

Rewrite the expression.

$\frac{1}{5 x^{3}} \cdot \frac{15 x^{2}}{2}$

Step 3

Cancel the common factor of $5 x^{2}$ .

Factor $5 x^{2}$ out of $5 x^{3}$ .

$\frac{1}{5 x^{2} (x)} \cdot \frac{15 x^{2}}{2}$

Factor $5 x^{2}$ out of $15 x^{2}$ .

$\frac{1}{5 x^{2} (x)} \cdot \frac{5 x^{2} (3)}{2}$

Cancel the common factor.

$\frac{1}{5 x^{2} x} \cdot \frac{5 x^{2} \cdot 3}{2}$

Rewrite the expression.

$\frac{1}{x} \cdot \frac{3}{2}$

Step 4

Multiply $\frac{1}{x}$ by $\frac{3}{2}$ .

$\frac{3}{x \cdot 2}$

Step 5

Move $2$ to the left of $x$ .

$\frac{3}{2 x}$