Basic Math Examples

$\frac{- 3}{2 a^{3} b^{2}} - \frac{7}{3 a b^{4}}$

Step 1

Move the negative in front of the fraction.

$- \frac{3}{2 a^{3} b^{2}} - \frac{7}{3 a b^{4}}$

Step 2

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

$- \frac{3}{2 a^{3} b^{2}} \cdot \frac{3 b^{2}}{3 b^{2}} - \frac{7}{3 a b^{4}}$

Step 3

To write $- \frac{7}{3 a b^{4}}$ as a fraction with a common denominator, multiply by $\frac{2 a^{2}}{2 a^{2}}$ .

$- \frac{3}{2 a^{3} b^{2}} \cdot \frac{3 b^{2}}{3 b^{2}} - \frac{7}{3 a b^{4}} \cdot \frac{2 a^{2}}{2 a^{2}}$

Step 4

Write each expression with a common denominator of $6 a^{3} b^{4}$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{3}{2 a^{3} b^{2}}$ by $\frac{3 b^{2}}{3 b^{2}}$ .

$- \frac{3 (3 b^{2})}{2 a^{3} b^{2} (3 b^{2})} - \frac{7}{3 a b^{4}} \cdot \frac{2 a^{2}}{2 a^{2}}$

Step 4.2

Multiply $3$ by $2$ .

$- \frac{3 (3 b^{2})}{6 a^{3} b^{2} b^{2}} - \frac{7}{3 a b^{4}} \cdot \frac{2 a^{2}}{2 a^{2}}$

Step 4.3

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

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Step 4.3.1

Move $b^{2}$ .

$- \frac{3 (3 b^{2})}{6 a^{3} (b^{2} b^{2})} - \frac{7}{3 a b^{4}} \cdot \frac{2 a^{2}}{2 a^{2}}$

Step 4.3.2

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

$- \frac{3 (3 b^{2})}{6 a^{3} b^{2 + 2}} - \frac{7}{3 a b^{4}} \cdot \frac{2 a^{2}}{2 a^{2}}$

Step 4.3.3

Add $2$ and $2$ .

$- \frac{3 (3 b^{2})}{6 a^{3} b^{4}} - \frac{7}{3 a b^{4}} \cdot \frac{2 a^{2}}{2 a^{2}}$

Step 4.4

Multiply $\frac{7}{3 a b^{4}}$ by $\frac{2 a^{2}}{2 a^{2}}$ .

$- \frac{3 (3 b^{2})}{6 a^{3} b^{4}} - \frac{7 (2 a^{2})}{3 a b^{4} (2 a^{2})}$

Step 4.5

Multiply $2$ by $3$ .

$- \frac{3 (3 b^{2})}{6 a^{3} b^{4}} - \frac{7 (2 a^{2})}{6 a b^{4} a^{2}}$

Step 4.6

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

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Step 4.6.1

Move $a^{2}$ .

$- \frac{3 (3 b^{2})}{6 a^{3} b^{4}} - \frac{7 (2 a^{2})}{6 (a^{2} a) b^{4}}$

Step 4.6.2

Multiply $a^{2}$ by $a$ .

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Step 4.6.2.1

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

$- \frac{3 (3 b^{2})}{6 a^{3} b^{4}} - \frac{7 (2 a^{2})}{6 (a^{2} a^{1}) b^{4}}$

Step 4.6.2.2

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

$- \frac{3 (3 b^{2})}{6 a^{3} b^{4}} - \frac{7 (2 a^{2})}{6 a^{2 + 1} b^{4}}$

Step 4.6.3

Add $2$ and $1$ .

$- \frac{3 (3 b^{2})}{6 a^{3} b^{4}} - \frac{7 (2 a^{2})}{6 a^{3} b^{4}}$

Step 5

Combine the numerators over the common denominator.

$\frac{- 3 (3 b^{2}) - 7 (2 a^{2})}{6 a^{3} b^{4}}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $- 3$ by $3$ .

$\frac{- 9 b^{2} - 7 \cdot 2 a^{2}}{6 a^{3} b^{4}}$

Step 6.2

Multiply $- 7$ by $2$ .

$\frac{- 9 b^{2} - 14 a^{2}}{6 a^{3} b^{4}}$

Step 7

Simplify with factoring out.

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Step 7.1

Factor $- 1$ out of $- 9 b^{2}$ .

$\frac{- (9 b^{2}) - 14 a^{2}}{6 a^{3} b^{4}}$

Step 7.2

Factor $- 1$ out of $- 14 a^{2}$ .

$\frac{- (9 b^{2}) - (14 a^{2})}{6 a^{3} b^{4}}$

Step 7.3

Factor $- 1$ out of $- (9 b^{2}) - (14 a^{2})$ .

$\frac{- (9 b^{2} + 14 a^{2})}{6 a^{3} b^{4}}$

Step 7.4

Simplify the expression.

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Step 7.4.1

Rewrite $- (9 b^{2} + 14 a^{2})$ as $- 1 (9 b^{2} + 14 a^{2})$ .

$\frac{- 1 (9 b^{2} + 14 a^{2})}{6 a^{3} b^{4}}$

Step 7.4.2

Move the negative in front of the fraction.

$- \frac{9 b^{2} + 14 a^{2}}{6 a^{3} b^{4}}$