Simplify (7x+4)/(8y)-(3x-1)/(6y)

$\frac{7 x + 4}{8 y} - \frac{3 x - 1}{6 y}$

To write $\frac{7 x + 4}{8 y}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{7 x + 4}{8 y} \cdot \frac{3}{3} - \frac{3 x - 1}{6 y}$

To write $- \frac{3 x - 1}{6 y}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{7 x + 4}{8 y} \cdot \frac{3}{3} - \frac{3 x - 1}{6 y} \cdot \frac{4}{4}$

Write each expression with a common denominator of $24 y$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{7 x + 4}{8 y}$ by $\frac{3}{3}$ .

$\frac{(7 x + 4) \cdot 3}{8 y \cdot 3} - \frac{3 x - 1}{6 y} \cdot \frac{4}{4}$

Multiply $3$ by $8$ .

$\frac{(7 x + 4) \cdot 3}{24 y} - \frac{3 x - 1}{6 y} \cdot \frac{4}{4}$

Multiply $\frac{3 x - 1}{6 y}$ by $\frac{4}{4}$ .

$\frac{(7 x + 4) \cdot 3}{24 y} - \frac{(3 x - 1) \cdot 4}{6 y \cdot 4}$

Multiply $4$ by $6$ .

$\frac{(7 x + 4) \cdot 3}{24 y} - \frac{(3 x - 1) \cdot 4}{24 y}$

Combine the numerators over the common denominator.

$\frac{(7 x + 4) \cdot 3 - (3 x - 1) \cdot 4}{24 y}$

Simplify the numerator.

Apply the distributive property.

$\frac{7 x \cdot 3 + 4 \cdot 3 - (3 x - 1) \cdot 4}{24 y}$

Multiply $3$ by $7$ .

$\frac{21 x + 4 \cdot 3 - (3 x - 1) \cdot 4}{24 y}$

Multiply $4$ by $3$ .

$\frac{21 x + 12 - (3 x - 1) \cdot 4}{24 y}$

Apply the distributive property.

$\frac{21 x + 12 + (- (3 x) - - 1) \cdot 4}{24 y}$

Multiply $3$ by $- 1$ .

$\frac{21 x + 12 + (- 3 x - - 1) \cdot 4}{24 y}$

Multiply $- 1$ by $- 1$ .

$\frac{21 x + 12 + (- 3 x + 1) \cdot 4}{24 y}$

Apply the distributive property.

$\frac{21 x + 12 - 3 x \cdot 4 + 1 \cdot 4}{24 y}$

Multiply $4$ by $- 3$ .

$\frac{21 x + 12 - 12 x + 1 \cdot 4}{24 y}$

Multiply $4$ by $1$ .

$\frac{21 x + 12 - 12 x + 4}{24 y}$

Subtract $12 x$ from $21 x$ .

$\frac{9 x + 12 + 4}{24 y}$

Add $12$ and $4$ .

$\frac{9 x + 16}{24 y}$