Simplify (4y)/(xy)-(2x)/(xy^3)

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

Step 1

Simplify each term.

Cancel the common factor of $y$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

To write $\frac{4}{x}$ as a fraction with a common denominator, multiply by $\frac{y^{3}}{y^{3}}$ .

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

Step 3

To write $- \frac{2}{y^{3}}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

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

Step 4

Write each expression with a common denominator of $x y^{3}$ , by multiplying each by an appropriate factor of $1$ .

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

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

Multiply $\frac{2}{y^{3}}$ by $\frac{x}{x}$ .

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

Reorder the factors of $x y^{3}$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Factor $2$ out of $4 y^{3} - 2 x$ .

Factor $2$ out of $4 y^{3}$ .

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

Factor $2$ out of $- 2 x$ .

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

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

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