Simplify (6/y-4/x)/y

$\frac{\frac{6}{y} - \frac{4}{x}}{y}$

Step 1

Simplify the numerator.

To write $\frac{6}{y}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{\frac{6}{y} \cdot \frac{x}{x} - \frac{4}{x}}{y}$

To write $- \frac{4}{x}$ as a fraction with a common denominator, multiply by $\frac{y}{y}$ .

$\frac{\frac{6}{y} \cdot \frac{x}{x} - \frac{4}{x} \cdot \frac{y}{y}}{y}$

Write each expression with a common denominator of $y x$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{6}{y}$ by $\frac{x}{x}$ .

$\frac{\frac{6 x}{y x} - \frac{4}{x} \cdot \frac{y}{y}}{y}$

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

$\frac{\frac{6 x}{y x} - \frac{4 y}{x y}}{y}$

Reorder the factors of $y x$ .

$\frac{\frac{6 x}{x y} - \frac{4 y}{x y}}{y}$

Combine the numerators over the common denominator.

$\frac{\frac{6 x - 4 y}{x y}}{y}$

Factor $2$ out of $6 x - 4 y$ .

Factor $2$ out of $6 x$ .

$\frac{\frac{2 (3 x) - 4 y}{x y}}{y}$

Factor $2$ out of $- 4 y$ .

$\frac{\frac{2 (3 x) + 2 (- 2 y)}{x y}}{y}$

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

$\frac{\frac{2 (3 x - 2 y)}{x y}}{y}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{2 (3 x - 2 y)}{x y} \cdot \frac{1}{y}$

Step 3

Multiply $\frac{2 (3 x - 2 y)}{x y} \cdot \frac{1}{y}$ .

Multiply $\frac{2 (3 x - 2 y)}{x y}$ by $\frac{1}{y}$ .

$\frac{2 (3 x - 2 y)}{x y \cdot y}$

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

$\frac{2 (3 x - 2 y)}{x (y^{1} y)}$

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

$\frac{2 (3 x - 2 y)}{x (y^{1} y^{1})}$

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

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

Add $1$ and $1$ .

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