Simplify (2- square root of 6)/(4+ square root of 6)

$\frac{2 - \sqrt{6}}{4 + \sqrt{6}}$

Multiply $\frac{2 - \sqrt{6}}{4 + \sqrt{6}}$ by $\frac{4 - \sqrt{6}}{4 - \sqrt{6}}$ .

$\frac{2 - \sqrt{6}}{4 + \sqrt{6}} \cdot \frac{4 - \sqrt{6}}{4 - \sqrt{6}}$

Combine fractions.

Multiply $\frac{2 - \sqrt{6}}{4 + \sqrt{6}}$ by $\frac{4 - \sqrt{6}}{4 - \sqrt{6}}$ .

$\frac{(2 - \sqrt{6}) (4 - \sqrt{6})}{(4 + \sqrt{6}) (4 - \sqrt{6})}$

Expand the denominator using the FOIL method.

$\frac{(2 - \sqrt{6}) (4 - \sqrt{6})}{16 - 4 \sqrt{6} + \sqrt{6} \cdot 4 - {\sqrt{6}}^{2}}$

Simplify.

$\frac{(2 - \sqrt{6}) (4 - \sqrt{6})}{10}$

Expand $(2 - \sqrt{6}) (4 - \sqrt{6})$ using the FOIL Method.

Apply the distributive property.

$\frac{2 (4 - \sqrt{6}) - \sqrt{6} (4 - \sqrt{6})}{10}$

Apply the distributive property.

$\frac{2 \cdot 4 + 2 (- \sqrt{6}) - \sqrt{6} (4 - \sqrt{6})}{10}$

Apply the distributive property.

$\frac{2 \cdot 4 + 2 (- \sqrt{6}) - \sqrt{6} \cdot 4 - \sqrt{6} (- \sqrt{6})}{10}$

Simplify and combine like terms.

Simplify each term.

Multiply $2$ by $4$ .

$\frac{8 + 2 (- \sqrt{6}) - \sqrt{6} \cdot 4 - \sqrt{6} (- \sqrt{6})}{10}$

Multiply $- 1$ by $2$ .

$\frac{8 - 2 \sqrt{6} - \sqrt{6} \cdot 4 - \sqrt{6} (- \sqrt{6})}{10}$

Multiply $4$ by $- 1$ .

$\frac{8 - 2 \sqrt{6} - 4 \sqrt{6} - \sqrt{6} (- \sqrt{6})}{10}$

Multiply $- \sqrt{6} (- \sqrt{6})$ .

Multiply $- 1$ by $- 1$ .

$\frac{8 - 2 \sqrt{6} - 4 \sqrt{6} + 1 \sqrt{6} \sqrt{6}}{10}$

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

$\frac{8 - 2 \sqrt{6} - 4 \sqrt{6} + \sqrt{6} \sqrt{6}}{10}$

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

$\frac{8 - 2 \sqrt{6} - 4 \sqrt{6} + {\sqrt{6}}^{1} \sqrt{6}}{10}$

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

$\frac{8 - 2 \sqrt{6} - 4 \sqrt{6} + {\sqrt{6}}^{1} {\sqrt{6}}^{1}}{10}$

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

$\frac{8 - 2 \sqrt{6} - 4 \sqrt{6} + {\sqrt{6}}^{1 + 1}}{10}$

Add $1$ and $1$ .

$\frac{8 - 2 \sqrt{6} - 4 \sqrt{6} + {\sqrt{6}}^{2}}{10}$

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

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

$\frac{8 - 2 \sqrt{6} - 4 \sqrt{6} + {(6^{\frac{1}{2}})}^{2}}{10}$

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

$\frac{8 - 2 \sqrt{6} - 4 \sqrt{6} + 6^{\frac{1}{2} \cdot 2}}{10}$

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

$\frac{8 - 2 \sqrt{6} - 4 \sqrt{6} + 6^{\frac{2}{2}}}{10}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{8 - 2 \sqrt{6} - 4 \sqrt{6} + 6^{\frac{2}{2}}}{10}$

Rewrite the expression.

$\frac{8 - 2 \sqrt{6} - 4 \sqrt{6} + 6^{1}}{10}$

Evaluate the exponent.

$\frac{8 - 2 \sqrt{6} - 4 \sqrt{6} + 6}{10}$

Add $8$ and $6$ .

$\frac{14 - 2 \sqrt{6} - 4 \sqrt{6}}{10}$

Subtract $4 \sqrt{6}$ from $- 2 \sqrt{6}$ .

$\frac{14 - 6 \sqrt{6}}{10}$

Cancel the common factor of $14 - 6 \sqrt{6}$ and $10$ .

Factor $2$ out of $14$ .

$\frac{2 (7) - 6 \sqrt{6}}{10}$

Factor $2$ out of $- 6 \sqrt{6}$ .

$\frac{2 (7) + 2 (- 3 \sqrt{6})}{10}$

Factor $2$ out of $2 (7) + 2 (- 3 \sqrt{6})$ .

$\frac{2 (7 - 3 \sqrt{6})}{10}$

Cancel the common factors.

Factor $2$ out of $10$ .

$\frac{2 (7 - 3 \sqrt{6})}{2 \cdot 5}$

Cancel the common factor.

$\frac{2 (7 - 3 \sqrt{6})}{2 \cdot 5}$

Rewrite the expression.

$\frac{7 - 3 \sqrt{6}}{5}$

The result can be shown in multiple forms.

Exact Form:

$\frac{7 - 3 \sqrt{6}}{5}$

Decimal Form:

$- 0.06969384 \dots$

Simplify (2- square root of 6)/(4+ square root of 6)

Related Questions

Support LCMGCF.com by disabling your adblocker.