Algebra Examples

$\frac{2}{a^{2} b^{3}} + \frac{- 2}{a b}$

Step 1

Move the negative in front of the fraction.

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

Step 2

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

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

Step 3

Write each expression with a common denominator of $a^{2} b^{3}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

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

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

Step 3.2

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

$\frac{2}{a^{2} b^{3}} - \frac{2 (a b^{2})}{a^{1} a b \cdot b^{2}}$

Step 3.3

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

$\frac{2}{a^{2} b^{3}} - \frac{2 (a b^{2})}{a^{1} a^{1} b \cdot b^{2}}$

Step 3.4

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

$\frac{2}{a^{2} b^{3}} - \frac{2 (a b^{2})}{a^{1 + 1} b \cdot b^{2}}$

Step 3.5

Add $1$ and $1$ .

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

Step 3.6

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

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Step 3.6.1

Move $b^{2}$ .

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

Step 3.6.2

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

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Step 3.6.2.1

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

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

Step 3.6.2.2

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

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

Step 3.6.3

Add $2$ and $1$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Factor $2$ out of $2 - 2 a b^{2}$ .

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Step 5.1

Factor $2$ out of $2$ .

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

Step 5.2

Factor $2$ out of $- 2 a b^{2}$ .

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

Step 5.3

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

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