Simplify ((5x)/(2x+3))÷((x+1)/(3x))

$\frac{5 x}{2 x + 3} \div \frac{x + 1}{3 x}$

To divide by a fraction, multiply by its reciprocal.

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

Multiply $\frac{5 x}{2 x + 3} \cdot \frac{3 x}{x + 1}$ .

Multiply $\frac{5 x}{2 x + 3}$ by $\frac{3 x}{x + 1}$ .

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

Multiply $3$ by $5$ .

$\frac{15 x \cdot x}{(2 x + 3) (x + 1)}$

Raise $x$ to the power of $1$ .

$\frac{15 (x^{1} x)}{(2 x + 3) (x + 1)}$

Raise $x$ to the power of $1$ .

$\frac{15 (x^{1} x^{1})}{(2 x + 3) (x + 1)}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{15 x^{1 + 1}}{(2 x + 3) (x + 1)}$

Add $1$ and $1$ .

$\frac{15 x^{2}}{(2 x + 3) (x + 1)}$