Finite Math Examples

$\frac{5 - \frac{1}{7 v}}{2 + \frac{1}{7 v}}$

Step 1

Multiply the numerator and denominator of the fraction by $7 v$ .

Tap for more steps...

Step 1.1

Multiply $\frac{5 - \frac{1}{7 v}}{2 + \frac{1}{7 v}}$ by $\frac{7 v}{7 v}$ .

$\frac{7 v}{7 v} \cdot \frac{5 - \frac{1}{7 v}}{2 + \frac{1}{7 v}}$

Step 1.2

Combine.

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

Step 2

Apply the distributive property.

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

Step 3

Simplify by cancelling.

Tap for more steps...

Step 3.1

Cancel the common factor of $7 v$ .

Tap for more steps...

Step 3.1.1

Move the leading negative in $- \frac{1}{7 v}$ into the numerator.

$\frac{7 v \cdot 5 + 7 v \frac{- 1}{7 v}}{7 v \cdot 2 + 7 v \frac{1}{7 v}}$

Step 3.1.2

Cancel the common factor.

$\frac{7 v \cdot 5 + 7 v \frac{- 1}{7 v}}{7 v \cdot 2 + 7 v \frac{1}{7 v}}$

Step 3.1.3

Rewrite the expression.

$\frac{7 v \cdot 5 - 1}{7 v \cdot 2 + 7 v \frac{1}{7 v}}$

Step 3.2

Cancel the common factor of $7 v$ .

Tap for more steps...

Step 3.2.1

Cancel the common factor.

$\frac{7 v \cdot 5 - 1}{7 v \cdot 2 + 7 v \frac{1}{7 v}}$

Step 3.2.2

Rewrite the expression.

$\frac{7 v \cdot 5 - 1}{7 v \cdot 2 + 1}$

Step 4

Multiply.

Tap for more steps...

Step 4.1

Multiply $5$ by $7$ .

$\frac{35 v - 1}{7 v \cdot 2 + 1}$

Step 4.2

Multiply $2$ by $7$ .

$\frac{35 v - 1}{14 v + 1}$