Basic Math Examples

$\frac{- 4}{9 v^{2}} + \frac{5}{6 v^{3}}$

Step 1

Move the negative in front of the fraction.

$- \frac{4}{9 v^{2}} + \frac{5}{6 v^{3}}$

Step 2

To write $- \frac{4}{9 v^{2}}$ as a fraction with a common denominator, multiply by $\frac{2 v}{2 v}$ .

$- \frac{4}{9 v^{2}} \cdot \frac{2 v}{2 v} + \frac{5}{6 v^{3}}$

Step 3

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

$- \frac{4}{9 v^{2}} \cdot \frac{2 v}{2 v} + \frac{5}{6 v^{3}} \cdot \frac{3}{3}$

Step 4

Write each expression with a common denominator of $18 v^{3}$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 4.1

Multiply $\frac{4}{9 v^{2}}$ by $\frac{2 v}{2 v}$ .

$- \frac{4 (2 v)}{9 v^{2} (2 v)} + \frac{5}{6 v^{3}} \cdot \frac{3}{3}$

Step 4.2

Multiply $2$ by $9$ .

$- \frac{4 (2 v)}{18 v^{2} v} + \frac{5}{6 v^{3}} \cdot \frac{3}{3}$

Step 4.3

Raise $v$ to the power of $1$ .

$- \frac{4 (2 v)}{18 (v^{1} v^{2})} + \frac{5}{6 v^{3}} \cdot \frac{3}{3}$

Step 4.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- \frac{4 (2 v)}{18 v^{1 + 2}} + \frac{5}{6 v^{3}} \cdot \frac{3}{3}$

Step 4.5

Add $1$ and $2$ .

$- \frac{4 (2 v)}{18 v^{3}} + \frac{5}{6 v^{3}} \cdot \frac{3}{3}$

Step 4.6

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

$- \frac{4 (2 v)}{18 v^{3}} + \frac{5 \cdot 3}{6 v^{3} \cdot 3}$

Step 4.7

Multiply $3$ by $6$ .

$- \frac{4 (2 v)}{18 v^{3}} + \frac{5 \cdot 3}{18 v^{3}}$

Step 5

Combine the numerators over the common denominator.

$\frac{- 4 (2 v) + 5 \cdot 3}{18 v^{3}}$

Step 6

Simplify the numerator.

Tap for more steps...

Step 6.1

Multiply $- 4$ by $2$ .

$\frac{- 8 v + 5 \cdot 3}{18 v^{3}}$

Step 6.2

Multiply $5$ by $3$ .

$\frac{- 8 v + 15}{18 v^{3}}$

Step 7

Simplify with factoring out.

Tap for more steps...

Step 7.1

Factor $- 1$ out of $- 8 v$ .

$\frac{- (8 v) + 15}{18 v^{3}}$

Step 7.2

Rewrite $15$ as $- 1 (- 15)$ .

$\frac{- (8 v) - 1 (- 15)}{18 v^{3}}$

Step 7.3

Factor $- 1$ out of $- (8 v) - 1 (- 15)$ .

$\frac{- (8 v - 15)}{18 v^{3}}$

Step 7.4

Simplify the expression.

Tap for more steps...

Step 7.4.1

Rewrite $- (8 v - 15)$ as $- 1 (8 v - 15)$ .

$\frac{- 1 (8 v - 15)}{18 v^{3}}$

Step 7.4.2

Move the negative in front of the fraction.

$- \frac{8 v - 15}{18 v^{3}}$