Simplify (6 square root of 3-4)/(8- square root of 3)

$\frac{6 \sqrt{3} - 4}{8 - \sqrt{3}}$

Multiply $\frac{6 \sqrt{3} - 4}{8 - \sqrt{3}}$ by $\frac{8 + \sqrt{3}}{8 + \sqrt{3}}$ .

$\frac{6 \sqrt{3} - 4}{8 - \sqrt{3}} \cdot \frac{8 + \sqrt{3}}{8 + \sqrt{3}}$

Combine fractions.

Multiply $\frac{6 \sqrt{3} - 4}{8 - \sqrt{3}}$ by $\frac{8 + \sqrt{3}}{8 + \sqrt{3}}$ .

$\frac{(6 \sqrt{3} - 4) (8 + \sqrt{3})}{(8 - \sqrt{3}) (8 + \sqrt{3})}$

Expand the denominator using the FOIL method.

$\frac{(6 \sqrt{3} - 4) (8 + \sqrt{3})}{64 + 8 \sqrt{3} - 8 \sqrt{3} - {\sqrt{3}}^{2}}$

Simplify.

$\frac{(6 \sqrt{3} - 4) (8 + \sqrt{3})}{61}$

Expand $(6 \sqrt{3} - 4) (8 + \sqrt{3})$ using the FOIL Method.

Apply the distributive property.

$\frac{6 \sqrt{3} (8 + \sqrt{3}) - 4 (8 + \sqrt{3})}{61}$

Apply the distributive property.

$\frac{6 \sqrt{3} \cdot 8 + 6 \sqrt{3} \sqrt{3} - 4 (8 + \sqrt{3})}{61}$

Apply the distributive property.

$\frac{6 \sqrt{3} \cdot 8 + 6 \sqrt{3} \sqrt{3} - 4 \cdot 8 - 4 \sqrt{3}}{61}$

Simplify and combine like terms.

Simplify each term.

Multiply $8$ by $6$ .

$\frac{48 \sqrt{3} + 6 \sqrt{3} \sqrt{3} - 4 \cdot 8 - 4 \sqrt{3}}{61}$

Multiply $6 \sqrt{3} \sqrt{3}$ .

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

$\frac{48 \sqrt{3} + 6 ({\sqrt{3}}^{1} \sqrt{3}) - 4 \cdot 8 - 4 \sqrt{3}}{61}$

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

$\frac{48 \sqrt{3} + 6 ({\sqrt{3}}^{1} {\sqrt{3}}^{1}) - 4 \cdot 8 - 4 \sqrt{3}}{61}$

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

$\frac{48 \sqrt{3} + 6 {\sqrt{3}}^{1 + 1} - 4 \cdot 8 - 4 \sqrt{3}}{61}$

Add $1$ and $1$ .

$\frac{48 \sqrt{3} + 6 {\sqrt{3}}^{2} - 4 \cdot 8 - 4 \sqrt{3}}{61}$

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

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

$\frac{48 \sqrt{3} + 6 {(3^{\frac{1}{2}})}^{2} - 4 \cdot 8 - 4 \sqrt{3}}{61}$

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

$\frac{48 \sqrt{3} + 6 \cdot 3^{\frac{1}{2} \cdot 2} - 4 \cdot 8 - 4 \sqrt{3}}{61}$

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

$\frac{48 \sqrt{3} + 6 \cdot 3^{\frac{2}{2}} - 4 \cdot 8 - 4 \sqrt{3}}{61}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{48 \sqrt{3} + 6 \cdot 3^{\frac{2}{2}} - 4 \cdot 8 - 4 \sqrt{3}}{61}$

Rewrite the expression.

$\frac{48 \sqrt{3} + 6 \cdot 3^{1} - 4 \cdot 8 - 4 \sqrt{3}}{61}$

Evaluate the exponent.

$\frac{48 \sqrt{3} + 6 \cdot 3 - 4 \cdot 8 - 4 \sqrt{3}}{61}$

Multiply $6$ by $3$ .

$\frac{48 \sqrt{3} + 18 - 4 \cdot 8 - 4 \sqrt{3}}{61}$

Multiply $- 4$ by $8$ .

$\frac{48 \sqrt{3} + 18 - 32 - 4 \sqrt{3}}{61}$

Subtract $4 \sqrt{3}$ from $48 \sqrt{3}$ .

$\frac{18 - 32 + 44 \sqrt{3}}{61}$

Subtract $32$ from $18$ .

$\frac{- 14 + 44 \sqrt{3}}{61}$

Rewrite $- 14$ as $- 1 (14)$ .

$\frac{- 1 (14) + 44 \sqrt{3}}{61}$

Factor $- 1$ out of $44 \sqrt{3}$ .

$\frac{- 1 (14) - (- 44 \sqrt{3})}{61}$

Factor $- 1$ out of $- 1 (14) - (- 44 \sqrt{3})$ .

$\frac{- 1 (14 - 44 \sqrt{3})}{61}$

Move the negative in front of the fraction.

$- \frac{14 - 44 \sqrt{3}}{61}$

The result can be shown in multiple forms.

Exact Form:

$- \frac{14 - 44 \sqrt{3}}{61}$

Decimal Form:

$1.01983992 \dots$

Simplify (6 square root of 3-4)/(8- square root of 3)

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