Simplify (6x)/(4/y-3/x)

$\frac{6 x}{\frac{4}{y} - \frac{3}{x}}$

Step 1

Simplify the denominator.

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

$\frac{6 x}{\frac{4}{y} \cdot \frac{x}{x} - \frac{3}{x}}$

To write $- \frac{3}{x}$ as a fraction with a common denominator, multiply by $\frac{y}{y}$ .

$\frac{6 x}{\frac{4}{y} \cdot \frac{x}{x} - \frac{3}{x} \cdot \frac{y}{y}}$

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

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

$\frac{6 x}{\frac{4 x}{y x} - \frac{3}{x} \cdot \frac{y}{y}}$

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

$\frac{6 x}{\frac{4 x}{y x} - \frac{3 y}{x y}}$

Reorder the factors of $y x$ .

$\frac{6 x}{\frac{4 x}{x y} - \frac{3 y}{x y}}$

Combine the numerators over the common denominator.

$\frac{6 x}{\frac{4 x - 3 y}{x y}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$6 x \frac{x y}{4 x - 3 y}$

Step 3

Multiply $6 x \frac{x y}{4 x - 3 y}$ .

Combine $6$ and $\frac{x y}{4 x - 3 y}$ .

$x \frac{6 (x y)}{4 x - 3 y}$

Combine $x$ and $\frac{6 (x y)}{4 x - 3 y}$ .

$\frac{x (6 (x y))}{4 x - 3 y}$

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

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

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

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

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

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

Add $1$ and $1$ .

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

$\frac{6 x^{2} y}{4 x - 3 y}$