Simplify (7v)/8-(8v-4)/(5v-2)

$\frac{7 v}{8} - \frac{8 v - 4}{5 v - 2}$

Step 1

Factor $4$ out of $8 v - 4$ .

Factor $4$ out of $8 v$ .

$\frac{7 v}{8} - \frac{4 (2 v) - 4}{5 v - 2}$

Factor $4$ out of $- 4$ .

$\frac{7 v}{8} - \frac{4 (2 v) + 4 (- 1)}{5 v - 2}$

Factor $4$ out of $4 (2 v) + 4 (- 1)$ .

$\frac{7 v}{8} - \frac{4 (2 v - 1)}{5 v - 2}$

Step 2

To write $\frac{7 v}{8}$ as a fraction with a common denominator, multiply by $\frac{5 v - 2}{5 v - 2}$ .

$\frac{7 v}{8} \cdot \frac{5 v - 2}{5 v - 2} - \frac{4 (2 v - 1)}{5 v - 2}$

Step 3

To write $- \frac{4 (2 v - 1)}{5 v - 2}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{7 v}{8} \cdot \frac{5 v - 2}{5 v - 2} - \frac{4 (2 v - 1)}{5 v - 2} \cdot \frac{8}{8}$

Step 4

Write each expression with a common denominator of $8 (5 v - 2)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{7 v}{8}$ by $\frac{5 v - 2}{5 v - 2}$ .

$\frac{7 v (5 v - 2)}{8 (5 v - 2)} - \frac{4 (2 v - 1)}{5 v - 2} \cdot \frac{8}{8}$

Multiply $\frac{4 (2 v - 1)}{5 v - 2}$ by $\frac{8}{8}$ .

$\frac{7 v (5 v - 2)}{8 (5 v - 2)} - \frac{4 (2 v - 1) \cdot 8}{(5 v - 2) \cdot 8}$

Reorder the factors of $(5 v - 2) \cdot 8$ .

$\frac{7 v (5 v - 2)}{8 (5 v - 2)} - \frac{4 (2 v - 1) \cdot 8}{8 (5 v - 2)}$

Step 5

Combine the numerators over the common denominator.

$\frac{7 v (5 v - 2) - 4 (2 v - 1) \cdot 8}{8 (5 v - 2)}$

Step 6

Simplify the numerator.

Apply the distributive property.

$\frac{7 v (5 v) + 7 v \cdot - 2 - 4 (2 v - 1) \cdot 8}{8 (5 v - 2)}$

Rewrite using the commutative property of multiplication.

$\frac{7 \cdot 5 v \cdot v + 7 v \cdot - 2 - 4 (2 v - 1) \cdot 8}{8 (5 v - 2)}$

Multiply $- 2$ by $7$ .

$\frac{7 \cdot 5 v \cdot v - 14 v - 4 (2 v - 1) \cdot 8}{8 (5 v - 2)}$

Simplify each term.

Multiply $v$ by $v$ by adding the exponents.

Move $v$ .

$\frac{7 \cdot 5 (v \cdot v) - 14 v - 4 (2 v - 1) \cdot 8}{8 (5 v - 2)}$

Multiply $v$ by $v$ .

$\frac{7 \cdot 5 v^{2} - 14 v - 4 (2 v - 1) \cdot 8}{8 (5 v - 2)}$

Multiply $7$ by $5$ .

$\frac{35 v^{2} - 14 v - 4 (2 v - 1) \cdot 8}{8 (5 v - 2)}$

Apply the distributive property.

$\frac{35 v^{2} - 14 v + (- 4 (2 v) - 4 \cdot - 1) \cdot 8}{8 (5 v - 2)}$

Multiply $2$ by $- 4$ .

$\frac{35 v^{2} - 14 v + (- 8 v - 4 \cdot - 1) \cdot 8}{8 (5 v - 2)}$

Multiply $- 4$ by $- 1$ .

$\frac{35 v^{2} - 14 v + (- 8 v + 4) \cdot 8}{8 (5 v - 2)}$

Apply the distributive property.

$\frac{35 v^{2} - 14 v - 8 v \cdot 8 + 4 \cdot 8}{8 (5 v - 2)}$

Multiply $8$ by $- 8$ .

$\frac{35 v^{2} - 14 v - 64 v + 4 \cdot 8}{8 (5 v - 2)}$

Multiply $4$ by $8$ .

$\frac{35 v^{2} - 14 v - 64 v + 32}{8 (5 v - 2)}$

Subtract $64 v$ from $- 14 v$ .

$\frac{35 v^{2} - 78 v + 32}{8 (5 v - 2)}$

Simplify (7v)/8-(8v-4)/(5v-2)

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