Simplify (5x-3)/(4x)-1/(6x)

$\frac{5 x - 3}{4 x} - \frac{1}{6 x}$

Step 1

To write $\frac{5 x - 3}{4 x}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5 x - 3}{4 x} \cdot \frac{3}{3} - \frac{1}{6 x}$

Step 2

To write $- \frac{1}{6 x}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 x - 3}{4 x} \cdot \frac{3}{3} - \frac{1}{6 x} \cdot \frac{2}{2}$

Step 3

Write each expression with a common denominator of $12 x$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5 x - 3}{4 x}$ by $\frac{3}{3}$ .

$\frac{(5 x - 3) \cdot 3}{4 x \cdot 3} - \frac{1}{6 x} \cdot \frac{2}{2}$

Multiply $3$ by $4$ .

$\frac{(5 x - 3) \cdot 3}{12 x} - \frac{1}{6 x} \cdot \frac{2}{2}$

Multiply $\frac{1}{6 x}$ by $\frac{2}{2}$ .

$\frac{(5 x - 3) \cdot 3}{12 x} - \frac{2}{6 x \cdot 2}$

Multiply $2$ by $6$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

Apply the distributive property.

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

Multiply $3$ by $5$ .

$\frac{15 x - 3 \cdot 3 - 2}{12 x}$

Multiply $- 3$ by $3$ .

$\frac{15 x - 9 - 2}{12 x}$

Subtract $2$ from $- 9$ .

$\frac{15 x - 11}{12 x}$