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

Simplify each term.

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Step 3.1

Move the negative in front of the fraction.

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

Step 3.2

Move the negative in front of the fraction.

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

Step 4

To write $- \frac{6}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 5

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

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

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

Step 5.2

Multiply $5$ by $3$ .

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

Step 6

Combine the numerators over the common denominator.

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

Step 7

Simplify the numerator.

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Step 7.1

Multiply $- 6$ by $3$ .

$- \frac{v}{3} + \frac{- 18 + 4}{15}$

Step 7.2

Add $- 18$ and $4$ .

$- \frac{v}{3} + \frac{- 14}{15}$

Step 8

Move the negative in front of the fraction.

$- \frac{v}{3} - \frac{14}{15}$