Algebra Examples

$\frac{a^{- 2} + a^{- 1} + a^{0}}{a}$

Step 1

Simplify the numerator.

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Step 1.1

Factor $a^{- 2}$ out of $a^{- 2} + a^{- 1} + a^{0}$ .

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Step 1.1.1

Multiply by $1$ .

$\frac{a^{- 2} \cdot 1 + a^{- 1} + a^{0}}{a}$

Step 1.1.2

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

$\frac{a^{- 2} \cdot 1 + a^{- 2} a + a^{0}}{a}$

Step 1.1.3

Factor $a^{- 2}$ out of $a^{0}$ .

$\frac{a^{- 2} \cdot 1 + a^{- 2} a + a^{- 2} a^{2}}{a}$

Step 1.1.4

Factor $a^{- 2}$ out of $a^{- 2} \cdot 1 + a^{- 2} a$ .

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

Step 1.1.5

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

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

Step 1.2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Factor $\frac{1}{a^{2}}$ out of $\frac{\frac{1}{a^{2}} (1 + a + a^{2})}{a}$ .

$\frac{1}{a^{2}} \cdot \frac{1 + a + a^{2}}{a}$

Step 3

Multiply $\frac{1}{a^{2}} \cdot \frac{1 + a + a^{2}}{a}$ .

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Step 3.1

Multiply $\frac{1}{a^{2}}$ by $\frac{1 + a + a^{2}}{a}$ .

$\frac{1 + a + a^{2}}{a^{2} a}$

Step 3.2

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

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Step 3.2.1

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

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Step 3.2.1.1

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

$\frac{1 + a + a^{2}}{a^{2} a^{1}}$

Step 3.2.1.2

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

$\frac{1 + a + a^{2}}{a^{2 + 1}}$

Step 3.2.2

Add $2$ and $1$ .

$\frac{1 + a + a^{2}}{a^{3}}$