Simplify 5/(12x)-7/(18y)

$\frac{5}{12 x} - \frac{7}{18 y}$

Step 1

To write $\frac{5}{12 x}$ as a fraction with a common denominator, multiply by $\frac{3 y}{3 y}$ .

$\frac{5}{12 x} \cdot \frac{3 y}{3 y} - \frac{7}{18 y}$

Step 2

To write $- \frac{7}{18 y}$ as a fraction with a common denominator, multiply by $\frac{2 x}{2 x}$ .

$\frac{5}{12 x} \cdot \frac{3 y}{3 y} - \frac{7}{18 y} \cdot \frac{2 x}{2 x}$

Step 3

Write each expression with a common denominator of $36 x y$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5}{12 x}$ by $\frac{3 y}{3 y}$ .

$\frac{5 (3 y)}{12 x (3 y)} - \frac{7}{18 y} \cdot \frac{2 x}{2 x}$

Multiply $3$ by $12$ .

$\frac{5 (3 y)}{36 x y} - \frac{7}{18 y} \cdot \frac{2 x}{2 x}$

Multiply $\frac{7}{18 y}$ by $\frac{2 x}{2 x}$ .

$\frac{5 (3 y)}{36 x y} - \frac{7 (2 x)}{18 y (2 x)}$

Multiply $2$ by $18$ .

$\frac{5 (3 y)}{36 x y} - \frac{7 (2 x)}{36 y x}$

Reorder the factors of $36 y x$ .

$\frac{5 (3 y)}{36 x y} - \frac{7 (2 x)}{36 x y}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 (3 y) - 7 (2 x)}{36 x y}$

Step 5

Simplify the numerator.

Multiply $5$ by $3$ .

$\frac{15 y - 7 \cdot 2 x}{36 x y}$

Multiply $- 7$ by $2$ .

$\frac{15 y - 14 x}{36 x y}$