Basic Math Examples

$\frac{- 9}{8 v^{3}} - \frac{7}{6 v^{2}}$

Step 1

Move the negative in front of the fraction.

$- \frac{9}{8 v^{3}} - \frac{7}{6 v^{2}}$

Step 2

To write $- \frac{9}{8 v^{3}}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{9}{8 v^{3}} \cdot \frac{3}{3} - \frac{7}{6 v^{2}}$

Step 3

To write $- \frac{7}{6 v^{2}}$ as a fraction with a common denominator, multiply by $\frac{4 v}{4 v}$ .

$- \frac{9}{8 v^{3}} \cdot \frac{3}{3} - \frac{7}{6 v^{2}} \cdot \frac{4 v}{4 v}$

Step 4

Write each expression with a common denominator of $24 v^{3}$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{9}{8 v^{3}}$ by $\frac{3}{3}$ .

$- \frac{9 \cdot 3}{8 v^{3} \cdot 3} - \frac{7}{6 v^{2}} \cdot \frac{4 v}{4 v}$

Step 4.2

Multiply $3$ by $8$ .

$- \frac{9 \cdot 3}{24 v^{3}} - \frac{7}{6 v^{2}} \cdot \frac{4 v}{4 v}$

Step 4.3

Multiply $\frac{7}{6 v^{2}}$ by $\frac{4 v}{4 v}$ .

$- \frac{9 \cdot 3}{24 v^{3}} - \frac{7 (4 v)}{6 v^{2} (4 v)}$

Step 4.4

Multiply $4$ by $6$ .

$- \frac{9 \cdot 3}{24 v^{3}} - \frac{7 (4 v)}{24 v^{2} v}$

Step 4.5

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

$- \frac{9 \cdot 3}{24 v^{3}} - \frac{7 (4 v)}{24 (v^{1} v^{2})}$

Step 4.6

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

$- \frac{9 \cdot 3}{24 v^{3}} - \frac{7 (4 v)}{24 v^{1 + 2}}$

Step 4.7

Add $1$ and $2$ .

$- \frac{9 \cdot 3}{24 v^{3}} - \frac{7 (4 v)}{24 v^{3}}$

Step 5

Combine the numerators over the common denominator.

$\frac{- 9 \cdot 3 - 7 (4 v)}{24 v^{3}}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $- 9$ by $3$ .

$\frac{- 27 - 7 \cdot 4 v}{24 v^{3}}$

Step 6.2

Multiply $- 7$ by $4$ .

$\frac{- 27 - 28 v}{24 v^{3}}$

Step 7

Simplify with factoring out.

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Step 7.1

Rewrite $- 27$ as $- 1 (27)$ .

$\frac{- 1 (27) - 28 v}{24 v^{3}}$

Step 7.2

Factor $- 1$ out of $- 28 v$ .

$\frac{- 1 (27) - (28 v)}{24 v^{3}}$

Step 7.3

Factor $- 1$ out of $- 1 (27) - (28 v)$ .

$\frac{- 1 (27 + 28 v)}{24 v^{3}}$

Step 7.4

Move the negative in front of the fraction.

$- \frac{27 + 28 v}{24 v^{3}}$