Algebra Examples

$\frac{- 8 m}{15 v^{4}} - \frac{4}{25 m v^{2}}$

Step 1

Move the negative in front of the fraction.

$- \frac{8 m}{15 v^{4}} - \frac{4}{25 m v^{2}}$

Step 2

To write $- \frac{8 m}{15 v^{4}}$ as a fraction with a common denominator, multiply by $\frac{5 m}{5 m}$ .

$- \frac{8 m}{15 v^{4}} \cdot \frac{5 m}{5 m} - \frac{4}{25 m v^{2}}$

Step 3

To write $- \frac{4}{25 m v^{2}}$ as a fraction with a common denominator, multiply by $\frac{3 v^{2}}{3 v^{2}}$ .

$- \frac{8 m}{15 v^{4}} \cdot \frac{5 m}{5 m} - \frac{4}{25 m v^{2}} \cdot \frac{3 v^{2}}{3 v^{2}}$

Step 4

Write each expression with a common denominator of $75 m v^{4}$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{8 m}{15 v^{4}}$ by $\frac{5 m}{5 m}$ .

$- \frac{8 m (5 m)}{15 v^{4} (5 m)} - \frac{4}{25 m v^{2}} \cdot \frac{3 v^{2}}{3 v^{2}}$

Step 4.2

Multiply $5$ by $15$ .

$- \frac{8 m (5 m)}{75 v^{4} m} - \frac{4}{25 m v^{2}} \cdot \frac{3 v^{2}}{3 v^{2}}$

Step 4.3

Multiply $\frac{4}{25 m v^{2}}$ by $\frac{3 v^{2}}{3 v^{2}}$ .

$- \frac{8 m (5 m)}{75 v^{4} m} - \frac{4 (3 v^{2})}{25 m v^{2} (3 v^{2})}$

Step 4.4

Multiply $3$ by $25$ .

$- \frac{8 m (5 m)}{75 v^{4} m} - \frac{4 (3 v^{2})}{75 m v^{2} v^{2}}$

Step 4.5

Multiply $v^{2}$ by $v^{2}$ by adding the exponents.

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Step 4.5.1

Move $v^{2}$ .

$- \frac{8 m (5 m)}{75 v^{4} m} - \frac{4 (3 v^{2})}{75 m (v^{2} v^{2})}$

Step 4.5.2

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

$- \frac{8 m (5 m)}{75 v^{4} m} - \frac{4 (3 v^{2})}{75 m v^{2 + 2}}$

Step 4.5.3

Add $2$ and $2$ .

$- \frac{8 m (5 m)}{75 v^{4} m} - \frac{4 (3 v^{2})}{75 m v^{4}}$

Step 4.6

Reorder the factors of $75 m v^{4}$ .

$- \frac{8 m (5 m)}{75 v^{4} m} - \frac{4 (3 v^{2})}{75 v^{4} m}$

Step 5

Combine the numerators over the common denominator.

$\frac{- 8 m (5 m) - 4 (3 v^{2})}{75 v^{4} m}$

Step 6

Simplify the numerator.

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Step 6.1

Factor $4$ out of $- 8 m (5 m) - 4 \cdot 3 v^{2}$ .

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Step 6.1.1

Factor $4$ out of $- 8 m (5 m)$ .

$\frac{4 (- 2 m (5 m)) - 4 \cdot 3 v^{2}}{75 v^{4} m}$

Step 6.1.2

Factor $4$ out of $- 4 \cdot 3 v^{2}$ .

$\frac{4 (- 2 m (5 m)) + 4 (- 1 \cdot 3 v^{2})}{75 v^{4} m}$

Step 6.1.3

Factor $4$ out of $4 (- 2 m (5 m)) + 4 (- 1 \cdot 3 v^{2})$ .

$\frac{4 (- 2 m (5 m) - 1 \cdot 3 v^{2})}{75 v^{4} m}$

Step 6.2

Rewrite using the commutative property of multiplication.

$\frac{4 (- 2 \cdot 5 m \cdot m - 1 \cdot 3 v^{2})}{75 v^{4} m}$

Step 6.3

Multiply $m$ by $m$ by adding the exponents.

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Step 6.3.1

Move $m$ .

$\frac{4 (- 2 \cdot 5 (m \cdot m) - 1 \cdot 3 v^{2})}{75 v^{4} m}$

Step 6.3.2

Multiply $m$ by $m$ .

$\frac{4 (- 2 \cdot 5 m^{2} - 1 \cdot 3 v^{2})}{75 v^{4} m}$

Step 6.4

Multiply $- 2$ by $5$ .

$\frac{4 (- 10 m^{2} - 1 \cdot 3 v^{2})}{75 v^{4} m}$

Step 6.5

Multiply $- 1$ by $3$ .

$\frac{4 (- 10 m^{2} - 3 v^{2})}{75 v^{4} m}$

Step 7

Simplify with factoring out.

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Step 7.1

Factor $- 1$ out of $- 10 m^{2}$ .

$\frac{4 (- (10 m^{2}) - 3 v^{2})}{75 v^{4} m}$

Step 7.2

Factor $- 1$ out of $- 3 v^{2}$ .

$\frac{4 (- (10 m^{2}) - (3 v^{2}))}{75 v^{4} m}$

Step 7.3

Factor $- 1$ out of $- (10 m^{2}) - (3 v^{2})$ .

$\frac{4 (- (10 m^{2} + 3 v^{2}))}{75 v^{4} m}$

Step 7.4

Simplify the expression.

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Step 7.4.1

Rewrite $- (10 m^{2} + 3 v^{2})$ as $- 1 (10 m^{2} + 3 v^{2})$ .

$\frac{4 (- 1 (10 m^{2} + 3 v^{2}))}{75 v^{4} m}$

Step 7.4.2

Move the negative in front of the fraction.

$- \frac{4 (10 m^{2} + 3 v^{2})}{75 v^{4} m}$