Basic Math Examples

$- \frac{\sqrt{19}}{5} \div (- \frac{\sqrt{6}}{5})$

Step 1

To divide by a fraction, multiply by its reciprocal.

$- \frac{\sqrt{19}}{5} (- \frac{5}{\sqrt{6}})$

Step 2

Cancel the common factor of $5$ .

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Step 2.1

Move the leading negative in $- \frac{\sqrt{19}}{5}$ into the numerator.

$\frac{- \sqrt{19}}{5} (- \frac{5}{\sqrt{6}})$

Step 2.2

Move the leading negative in $- \frac{5}{\sqrt{6}}$ into the numerator.

$\frac{- \sqrt{19}}{5} \cdot \frac{- 5}{\sqrt{6}}$

Step 2.3

Factor $5$ out of $- 5$ .

$\frac{- \sqrt{19}}{5} \cdot \frac{5 (- 1)}{\sqrt{6}}$

Step 2.4

Cancel the common factor.

$\frac{- \sqrt{19}}{5} \cdot \frac{5 \cdot - 1}{\sqrt{6}}$

Step 2.5

Rewrite the expression.

$- \sqrt{19} \frac{- 1}{\sqrt{6}}$

Step 3

Combine $\frac{- 1}{\sqrt{6}}$ and $\sqrt{19}$ .

$- \frac{- \sqrt{19}}{\sqrt{6}}$

Step 4

Move the negative in front of the fraction.

$- - \frac{\sqrt{19}}{\sqrt{6}}$

Step 5

Multiply $\frac{\sqrt{19}}{\sqrt{6}}$ by $\frac{\sqrt{6}}{\sqrt{6}}$ .

$- - (\frac{\sqrt{19}}{\sqrt{6}} \cdot \frac{\sqrt{6}}{\sqrt{6}})$

Step 6

Combine and simplify the denominator.

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Step 6.1

Multiply $\frac{\sqrt{19}}{\sqrt{6}}$ by $\frac{\sqrt{6}}{\sqrt{6}}$ .

$- - \frac{\sqrt{19} \sqrt{6}}{\sqrt{6} \sqrt{6}}$

Step 6.2

Raise $\sqrt{6}$ to the power of $1$ .

$- - \frac{\sqrt{19} \sqrt{6}}{{\sqrt{6}}^{1} \sqrt{6}}$

Step 6.3

Raise $\sqrt{6}$ to the power of $1$ .

$- - \frac{\sqrt{19} \sqrt{6}}{{\sqrt{6}}^{1} {\sqrt{6}}^{1}}$

Step 6.4

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

$- - \frac{\sqrt{19} \sqrt{6}}{{\sqrt{6}}^{1 + 1}}$

Step 6.5

Add $1$ and $1$ .

$- - \frac{\sqrt{19} \sqrt{6}}{{\sqrt{6}}^{2}}$

Step 6.6

Rewrite ${\sqrt{6}}^{2}$ as $6$ .

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Step 6.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6}$ as $6^{\frac{1}{2}}$ .

$- - \frac{\sqrt{19} \sqrt{6}}{{(6^{\frac{1}{2}})}^{2}}$

Step 6.6.2

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

$- - \frac{\sqrt{19} \sqrt{6}}{6^{\frac{1}{2} \cdot 2}}$

Step 6.6.3

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

$- - \frac{\sqrt{19} \sqrt{6}}{6^{\frac{2}{2}}}$

Step 6.6.4

Cancel the common factor of $2$ .

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Step 6.6.4.1

Cancel the common factor.

$- - \frac{\sqrt{19} \sqrt{6}}{6^{\frac{2}{2}}}$

Step 6.6.4.2

Rewrite the expression.

$- - \frac{\sqrt{19} \sqrt{6}}{6^{1}}$

Step 6.6.5

Evaluate the exponent.

$- - \frac{\sqrt{19} \sqrt{6}}{6}$

Step 7

Simplify the numerator.

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Step 7.1

Combine using the product rule for radicals.

$- - \frac{\sqrt{19 \cdot 6}}{6}$

Step 7.2

Multiply $19$ by $6$ .

$- - \frac{\sqrt{114}}{6}$

Step 8

Multiply $- - \frac{\sqrt{114}}{6}$ .

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Step 8.1

Multiply $- 1$ by $- 1$ .

$1 \frac{\sqrt{114}}{6}$

Step 8.2

Multiply $\frac{\sqrt{114}}{6}$ by $1$ .

$\frac{\sqrt{114}}{6}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{114}}{6}$

Decimal Form:

$1.77951304 \dots$