Algebra Examples

$\frac{x^{- 1} + x^{- 1}}{2 x^{2}}$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{\frac{1}{x} + x^{- 1}}{2 x^{2}}$

Step 1.2

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

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

Step 1.3

Add $\frac{1}{x}$ and $\frac{1}{x}$ .

$\frac{2 \frac{1}{x}}{2 x^{2}}$

Step 2

Combine $2$ and $\frac{1}{x}$ .

$\frac{\frac{2}{x}}{2 x^{2}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{2}{x} \cdot \frac{1}{2 x^{2}}$

Step 4

Combine.

$\frac{2 \cdot 1}{x (2 x^{2})}$

Step 5

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

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Step 5.1

Move $x^{2}$ .

$\frac{2 \cdot 1}{x^{2} x \cdot 2}$

Step 5.2

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

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Step 5.2.1

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

$\frac{2 \cdot 1}{x^{2} x^{1} \cdot 2}$

Step 5.2.2

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

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

Step 5.3

Add $2$ and $1$ .

$\frac{2 \cdot 1}{x^{3} \cdot 2}$

Step 6

Multiply $2$ by $1$ .

$\frac{2}{x^{3} \cdot 2}$

Step 7

Cancel the common factor of $2$ .

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Step 7.1

Cancel the common factor.

$\frac{2}{x^{3} \cdot 2}$

Step 7.2

Rewrite the expression.

$\frac{1}{x^{3}}$