Simplify ((4x+1)/(6x))÷(x/(3x-1))

$\frac{4 x + 1}{6 x} \div \frac{x}{3 x - 1}$

To divide by a fraction, multiply by its reciprocal.

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

Multiply $\frac{4 x + 1}{6 x} \cdot \frac{3 x - 1}{x}$ .

Multiply $\frac{4 x + 1}{6 x}$ by $\frac{3 x - 1}{x}$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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