Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Multiply the numerator by the reciprocal of the denominator.

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

Step 1.2

Simplify the denominator.

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Step 1.2.1

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

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

Step 1.2.2

Combine the numerators over the common denominator.

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

Step 1.2.3

Add $- 1$ and $2$ .

$- \frac{1}{2} \cdot \frac{1}{\frac{1}{2}} - 1$

Step 1.3

Multiply the numerator by the reciprocal of the denominator.

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

Step 1.4

Cancel the common factor of $2$ .

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Step 1.4.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

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

Step 1.4.2

Factor $2$ out of $1 \cdot 2$ .

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

Step 1.4.3

Cancel the common factor.

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

Step 1.4.4

Rewrite the expression.

$- 1 - 1$

Step 2

Subtract $1$ from $- 1$ .

$- 2$