Algebra Examples

$\frac{- \frac{1}{2}}{\frac{- \sqrt{3}}{2}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$- \frac{1}{2} \cdot \frac{2}{- \sqrt{3}}$

Step 2

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.1

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

$\frac{- 1}{2} \cdot \frac{2}{- \sqrt{3}}$

Step 2.2

Cancel the common factor.

$\frac{- 1}{2} \cdot \frac{2}{- \sqrt{3}}$

Step 2.3

Rewrite the expression.

$- \frac{1}{- \sqrt{3}}$

Step 3

Cancel the common factor of $1$ and $- 1$ .

Tap for more steps...

Step 3.1

Rewrite $1$ as $- 1 (- 1)$ .

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

Step 3.2

Move the negative in front of the fraction.

$- - \frac{1}{\sqrt{3}}$

Step 4

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

$- - (\frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}})$

Step 5

Combine and simplify the denominator.

Tap for more steps...

Step 5.1

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

$- - \frac{\sqrt{3}}{\sqrt{3} \sqrt{3}}$

Step 5.2

Raise $\sqrt{3}$ to the power of $1$ .

$- - \frac{\sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}}$

Step 5.3

Raise $\sqrt{3}$ to the power of $1$ .

$- - \frac{\sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}}$

Step 5.4

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

$- - \frac{\sqrt{3}}{{\sqrt{3}}^{1 + 1}}$

Step 5.5

Add $1$ and $1$ .

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

Step 5.6

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

Tap for more steps...

Step 5.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

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

Step 5.6.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- - \frac{\sqrt{3}}{3^{\frac{1}{2} \cdot 2}}$

Step 5.6.3

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

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

Step 5.6.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 5.6.4.1

Cancel the common factor.

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

Step 5.6.4.2

Rewrite the expression.

$- - \frac{\sqrt{3}}{3^{1}}$

Step 5.6.5

Evaluate the exponent.

$- - \frac{\sqrt{3}}{3}$

Step 6

Multiply $- - \frac{\sqrt{3}}{3}$ .

Tap for more steps...

Step 6.1

Multiply $- 1$ by $- 1$ .

$1 \frac{\sqrt{3}}{3}$

Step 6.2

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

$\frac{\sqrt{3}}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{3}}{3}$

Decimal Form:

$0.57735026 \dots$