Divide (x+(4x)/y)/(7/(3x))

$\frac{x + \frac{4 x}{y}}{\frac{7}{3 x}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$(x + \frac{4 x}{y}) \frac{3 x}{7}$

Step 2

Apply the distributive property.

$x \frac{3 x}{7} + \frac{4 x}{y} \cdot \frac{3 x}{7}$

Step 3

Multiply $x \frac{3 x}{7}$ .

Combine $x$ and $\frac{3 x}{7}$ .

$\frac{x (3 x)}{7} + \frac{4 x}{y} \cdot \frac{3 x}{7}$

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

$\frac{3 (x^{1} x)}{7} + \frac{4 x}{y} \cdot \frac{3 x}{7}$

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

$\frac{3 (x^{1} x^{1})}{7} + \frac{4 x}{y} \cdot \frac{3 x}{7}$

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

$\frac{3 x^{1 + 1}}{7} + \frac{4 x}{y} \cdot \frac{3 x}{7}$

Add $1$ and $1$ .

$\frac{3 x^{2}}{7} + \frac{4 x}{y} \cdot \frac{3 x}{7}$

Step 4

Multiply $\frac{4 x}{y} \cdot \frac{3 x}{7}$ .

Multiply $\frac{4 x}{y}$ by $\frac{3 x}{7}$ .

$\frac{3 x^{2}}{7} + \frac{4 x (3 x)}{y \cdot 7}$

Multiply $3$ by $4$ .

$\frac{3 x^{2}}{7} + \frac{12 x \cdot x}{y \cdot 7}$

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

$\frac{3 x^{2}}{7} + \frac{12 (x^{1} x)}{y \cdot 7}$

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

$\frac{3 x^{2}}{7} + \frac{12 (x^{1} x^{1})}{y \cdot 7}$

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

$\frac{3 x^{2}}{7} + \frac{12 x^{1 + 1}}{y \cdot 7}$

Add $1$ and $1$ .

$\frac{3 x^{2}}{7} + \frac{12 x^{2}}{y \cdot 7}$

Step 5

Move $7$ to the left of $y$ .

$\frac{3 x^{2}}{7} + \frac{12 x^{2}}{7 y}$