Simplify (8v)/(28w+21)-(3v+10)/(4w+3)

$\frac{8 v}{28 w + 21} - \frac{3 v + 10}{4 w + 3}$

Factor $7$ out of $28 w + 21$ .

Factor $7$ out of $28 w$ .

$\frac{8 v}{7 (4 w) + 21} - \frac{3 v + 10}{4 w + 3}$

Factor $7$ out of $21$ .

$\frac{8 v}{7 (4 w) + 7 (3)} - \frac{3 v + 10}{4 w + 3}$

Factor $7$ out of $7 (4 w) + 7 (3)$ .

$\frac{8 v}{7 (4 w + 3)} - \frac{3 v + 10}{4 w + 3}$

To write $- \frac{3 v + 10}{4 w + 3}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{8 v}{7 (4 w + 3)} - \frac{3 v + 10}{4 w + 3} \cdot \frac{7}{7}$

Write each expression with a common denominator of $7 (4 w + 3)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3 v + 10}{4 w + 3}$ by $\frac{7}{7}$ .

$\frac{8 v}{7 (4 w + 3)} - \frac{(3 v + 10) \cdot 7}{(4 w + 3) \cdot 7}$

Reorder the factors of $(4 w + 3) \cdot 7$ .

$\frac{8 v}{7 (4 w + 3)} - \frac{(3 v + 10) \cdot 7}{7 (4 w + 3)}$

Combine the numerators over the common denominator.

$\frac{8 v - (3 v + 10) \cdot 7}{7 (4 w + 3)}$

Simplify the numerator.

Apply the distributive property.

$\frac{8 v + (- (3 v) - 1 \cdot 10) \cdot 7}{7 (4 w + 3)}$

Multiply $3$ by $- 1$ .

$\frac{8 v + (- 3 v - 1 \cdot 10) \cdot 7}{7 (4 w + 3)}$

Multiply $- 1$ by $10$ .

$\frac{8 v + (- 3 v - 10) \cdot 7}{7 (4 w + 3)}$

Apply the distributive property.

$\frac{8 v - 3 v \cdot 7 - 10 \cdot 7}{7 (4 w + 3)}$

Multiply $7$ by $- 3$ .

$\frac{8 v - 21 v - 10 \cdot 7}{7 (4 w + 3)}$

Multiply $- 10$ by $7$ .

$\frac{8 v - 21 v - 70}{7 (4 w + 3)}$

Subtract $21 v$ from $8 v$ .

$\frac{- 13 v - 70}{7 (4 w + 3)}$

Simplify with factoring out.

Factor $- 1$ out of $- 13 v$ .

$\frac{- (13 v) - 70}{7 (4 w + 3)}$

Rewrite $- 70$ as $- 1 (70)$ .

$\frac{- (13 v) - 1 (70)}{7 (4 w + 3)}$

Factor $- 1$ out of $- (13 v) - 1 (70)$ .

$\frac{- (13 v + 70)}{7 (4 w + 3)}$

Simplify the expression.

Rewrite $- (13 v + 70)$ as $- 1 (13 v + 70)$ .

$\frac{- 1 (13 v + 70)}{7 (4 w + 3)}$

Move the negative in front of the fraction.

$- \frac{13 v + 70}{7 (4 w + 3)}$