Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Simplify the denominator.

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Step 1.1.1

Write $1$ as a fraction with a common denominator.

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

Step 1.1.2

Combine the numerators over the common denominator.

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

Step 1.1.3

Subtract $1$ from $2$ .

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

Step 1.2

Multiply the numerator by the reciprocal of the denominator.

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

Step 1.3

Multiply $2$ by $1$ .

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

Step 2

Add $1$ and $2$ .

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

Step 3

Simplify each term.

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Step 3.1

Simplify the denominator.

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Step 3.1.1

Write $1$ as a fraction with a common denominator.

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

Step 3.1.2

Combine the numerators over the common denominator.

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

Step 3.1.3

Add $2$ and $1$ .

$3 (1 - \frac{1}{\frac{3}{2}})$

Step 3.2

Multiply the numerator by the reciprocal of the denominator.

$3 (1 - (1 (\frac{2}{3})))$

Step 3.3

Multiply $\frac{2}{3}$ by $1$ .

$3 (1 - \frac{2}{3})$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Write $1$ as a fraction with a common denominator.

$3 (\frac{3}{3} - \frac{2}{3})$

Step 4.2

Simplify the expression.

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Step 4.2.1

Combine the numerators over the common denominator.

$3 \frac{3 - 2}{3}$

Step 4.2.2

Subtract $2$ from $3$ .

$3 (\frac{1}{3})$

Step 4.3

Cancel the common factor of $3$ .

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Step 4.3.1

Cancel the common factor.

$3 (\frac{1}{3})$

Step 4.3.2

Rewrite the expression.

$1$