Simplify ((7x^2)/(2x+6))÷((3x-5)/(x+3))

$\frac{7 x^{2}}{2 x + 6} \div \frac{3 x - 5}{x + 3}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{7 x^{2}}{2 x + 6} \cdot \frac{x + 3}{3 x - 5}$

Step 2

Factor $2$ out of $2 x + 6$ .

Factor $2$ out of $2 x$ .

$\frac{7 x^{2}}{2 (x) + 6} \cdot \frac{x + 3}{3 x - 5}$

Factor $2$ out of $6$ .

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

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

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

Step 3

Cancel the common factor of $x + 3$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{7 x^{2}}{2} \cdot \frac{1}{3 x - 5}$

Step 4

Multiply $\frac{7 x^{2}}{2}$ by $\frac{1}{3 x - 5}$ .

$\frac{7 x^{2}}{2 (3 x - 5)}$