Basic Math Examples

$(a^{- 1} + b^{- 1}) \div 1 - (a^{- 1} - b^{- 1})$

Step 1

Simplify each term.

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Step 1.1

Rewrite the division as a fraction.

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

Step 1.2

Divide $a^{- 1} + b^{- 1}$ by $1$ .

$a^{- 1} + b^{- 1} - (a^{- 1} - b^{- 1})$

Step 1.3

Simplify each term.

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Step 1.3.1

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

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

Step 1.3.2

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

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

Step 1.4

Simplify each term.

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Step 1.4.1

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

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

Step 1.4.2

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

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

Step 1.5

Apply the distributive property.

$\frac{1}{a} + \frac{1}{b} - \frac{1}{a} - - \frac{1}{b}$

Step 1.6

Multiply $- - \frac{1}{b}$ .

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Step 1.6.1

Multiply $- 1$ by $- 1$ .

$\frac{1}{a} + \frac{1}{b} - \frac{1}{a} + 1 \frac{1}{b}$

Step 1.6.2

Multiply $\frac{1}{b}$ by $1$ .

$\frac{1}{a} + \frac{1}{b} - \frac{1}{a} + \frac{1}{b}$

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $\frac{1}{a} + \frac{1}{b} - \frac{1}{a} + \frac{1}{b}$ .

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Step 2.1.1

Subtract $\frac{1}{a}$ from $\frac{1}{a}$ .

$\frac{1}{b} + 0 + \frac{1}{b}$

Step 2.1.2

Add $\frac{1}{b}$ and $0$ .

$\frac{1}{b} + \frac{1}{b}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{1 + 1}{b}$

Step 2.3

Add $1$ and $1$ .

$\frac{2}{b}$