Simplify (4x)/7-(8x)/3

$\frac{4 x}{7} - \frac{8 x}{3}$

Step 1

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

$\frac{4 x}{7} \cdot \frac{3}{3} - \frac{8 x}{3}$

Step 2

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

$\frac{4 x}{7} \cdot \frac{3}{3} - \frac{8 x}{3} \cdot \frac{7}{7}$

Step 3

Write each expression with a common denominator of $21$ , by multiplying each by an appropriate factor of $1$ .

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

$\frac{4 x \cdot 3}{7 \cdot 3} - \frac{8 x}{3} \cdot \frac{7}{7}$

Multiply $7$ by $3$ .

$\frac{4 x \cdot 3}{21} - \frac{8 x}{3} \cdot \frac{7}{7}$

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

$\frac{4 x \cdot 3}{21} - \frac{8 x \cdot 7}{3 \cdot 7}$

Multiply $3$ by $7$ .

$\frac{4 x \cdot 3}{21} - \frac{8 x \cdot 7}{21}$

Step 4

Combine the numerators over the common denominator.

$\frac{4 x \cdot 3 - 8 x \cdot 7}{21}$

Step 5

Simplify the numerator.

Factor $4 x$ out of $4 x \cdot 3 - 8 x \cdot 7$ .

Factor $4 x$ out of $4 x \cdot 3$ .

$\frac{4 x (3) - 8 x \cdot 7}{21}$

Factor $4 x$ out of $- 8 x \cdot 7$ .

$\frac{4 x (3) + 4 x (- 2 \cdot 7)}{21}$

Factor $4 x$ out of $4 x (3) + 4 x (- 2 \cdot 7)$ .

$\frac{4 x (3 - 2 \cdot 7)}{21}$

Multiply $- 2$ by $7$ .

$\frac{4 x (3 - 14)}{21}$

Subtract $14$ from $3$ .

$\frac{4 x \cdot - 11}{21}$

Multiply $- 11$ by $4$ .

$\frac{- 44 x}{21}$

Step 6

Move the negative in front of the fraction.

$- \frac{44 x}{21}$