Algebra Examples

$- \frac{6}{5} - \frac{2}{3} v + \frac{4}{15} + \frac{1}{3} v$

Step 1

Simplify each term.

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Step 1.1

Combine $v$ and $\frac{2}{3}$ .

$- \frac{6}{5} - \frac{v \cdot 2}{3} + \frac{4}{15} + \frac{1}{3} v$

Step 1.2

Move $2$ to the left of $v$ .

$- \frac{6}{5} - \frac{2 \cdot v}{3} + \frac{4}{15} + \frac{1}{3} v$

Step 1.3

Combine $\frac{1}{3}$ and $v$ .

$- \frac{6}{5} - \frac{2 v}{3} + \frac{4}{15} + \frac{v}{3}$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{- 6}{5} + \frac{- 2 v + v}{3} + \frac{4}{15}$

Step 2.2

Add $- 2 v$ and $v$ .

$\frac{- 6}{5} + \frac{- v}{3} + \frac{4}{15}$

Step 3

Find the common denominator.

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Step 3.1

Multiply $\frac{- 6}{5}$ by $\frac{3}{3}$ .

$\frac{- 6}{5} \cdot \frac{3}{3} + \frac{- v}{3} + \frac{4}{15}$

Step 3.2

Multiply $\frac{- 6}{5}$ by $\frac{3}{3}$ .

$\frac{- 6 \cdot 3}{5 \cdot 3} + \frac{- v}{3} + \frac{4}{15}$

Step 3.3

Multiply $\frac{- v}{3}$ by $\frac{5}{5}$ .

$\frac{- 6 \cdot 3}{5 \cdot 3} + \frac{- v}{3} \cdot \frac{5}{5} + \frac{4}{15}$

Step 3.4

Multiply $\frac{- v}{3}$ by $\frac{5}{5}$ .

$\frac{- 6 \cdot 3}{5 \cdot 3} + \frac{- v \cdot 5}{3 \cdot 5} + \frac{4}{15}$

Step 3.5

Reorder the factors of $5 \cdot 3$ .

$\frac{- 6 \cdot 3}{3 \cdot 5} + \frac{- v \cdot 5}{3 \cdot 5} + \frac{4}{15}$

Step 3.6

Multiply $3$ by $5$ .

$\frac{- 6 \cdot 3}{15} + \frac{- v \cdot 5}{3 \cdot 5} + \frac{4}{15}$

Step 3.7

Multiply $3$ by $5$ .

$\frac{- 6 \cdot 3}{15} + \frac{- v \cdot 5}{15} + \frac{4}{15}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 6 \cdot 3 - v \cdot 5 + 4}{15}$

Step 5

Simplify each term.

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Step 5.1

Multiply $- 6$ by $3$ .

$\frac{- 18 - v \cdot 5 + 4}{15}$

Step 5.2

Multiply $5$ by $- 1$ .

$\frac{- 18 - 5 v + 4}{15}$

Step 6

Simplify with factoring out.

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Step 6.1

Add $- 18$ and $4$ .

$\frac{- 5 v - 14}{15}$

Step 6.2

Factor $- 1$ out of $- 5 v$ .

$\frac{- (5 v) - 14}{15}$

Step 6.3

Rewrite $- 14$ as $- 1 (14)$ .

$\frac{- (5 v) - 1 (14)}{15}$

Step 6.4

Factor $- 1$ out of $- (5 v) - 1 (14)$ .

$\frac{- (5 v + 14)}{15}$

Step 6.5

Simplify the expression.

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Step 6.5.1

Rewrite $- (5 v + 14)$ as $- 1 (5 v + 14)$ .

$\frac{- 1 (5 v + 14)}{15}$

Step 6.5.2

Move the negative in front of the fraction.

$- \frac{5 v + 14}{15}$