Simplify (2 square root of 11-3)/( square root of 11+4)

$\frac{2 \sqrt{11} - 3}{\sqrt{11} + 4}$

Multiply $\frac{2 \sqrt{11} - 3}{\sqrt{11} + 4}$ by $\frac{\sqrt{11} - 4}{\sqrt{11} - 4}$ .

$\frac{2 \sqrt{11} - 3}{\sqrt{11} + 4} \cdot \frac{\sqrt{11} - 4}{\sqrt{11} - 4}$

Combine fractions.

Multiply $\frac{2 \sqrt{11} - 3}{\sqrt{11} + 4}$ by $\frac{\sqrt{11} - 4}{\sqrt{11} - 4}$ .

$\frac{(2 \sqrt{11} - 3) (\sqrt{11} - 4)}{(\sqrt{11} + 4) (\sqrt{11} - 4)}$

Expand the denominator using the FOIL method.

$\frac{(2 \sqrt{11} - 3) (\sqrt{11} - 4)}{{\sqrt{11}}^{2} + \sqrt{11} \cdot - 4 + 4 \sqrt{11} - 16}$

Simplify.

$\frac{(2 \sqrt{11} - 3) (\sqrt{11} - 4)}{- 5}$

Expand $(2 \sqrt{11} - 3) (\sqrt{11} - 4)$ using the FOIL Method.

Apply the distributive property.

$\frac{2 \sqrt{11} (\sqrt{11} - 4) - 3 (\sqrt{11} - 4)}{- 5}$

Apply the distributive property.

$\frac{2 \sqrt{11} \sqrt{11} + 2 \sqrt{11} \cdot - 4 - 3 (\sqrt{11} - 4)}{- 5}$

Apply the distributive property.

$\frac{2 \sqrt{11} \sqrt{11} + 2 \sqrt{11} \cdot - 4 - 3 \sqrt{11} - 3 \cdot - 4}{- 5}$

Simplify and combine like terms.

Simplify each term.

Multiply $2 \sqrt{11} \sqrt{11}$ .

Raise $\sqrt{11}$ to the power of $1$ .

$\frac{2 ({\sqrt{11}}^{1} \sqrt{11}) + 2 \sqrt{11} \cdot - 4 - 3 \sqrt{11} - 3 \cdot - 4}{- 5}$

Raise $\sqrt{11}$ to the power of $1$ .

$\frac{2 ({\sqrt{11}}^{1} {\sqrt{11}}^{1}) + 2 \sqrt{11} \cdot - 4 - 3 \sqrt{11} - 3 \cdot - 4}{- 5}$

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

$\frac{2 {\sqrt{11}}^{1 + 1} + 2 \sqrt{11} \cdot - 4 - 3 \sqrt{11} - 3 \cdot - 4}{- 5}$

Add $1$ and $1$ .

$\frac{2 {\sqrt{11}}^{2} + 2 \sqrt{11} \cdot - 4 - 3 \sqrt{11} - 3 \cdot - 4}{- 5}$

Rewrite ${\sqrt{11}}^{2}$ as $11$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{11}$ as $11^{\frac{1}{2}}$ .

$\frac{2 {(11^{\frac{1}{2}})}^{2} + 2 \sqrt{11} \cdot - 4 - 3 \sqrt{11} - 3 \cdot - 4}{- 5}$

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

$\frac{2 \cdot 11^{\frac{1}{2} \cdot 2} + 2 \sqrt{11} \cdot - 4 - 3 \sqrt{11} - 3 \cdot - 4}{- 5}$

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

$\frac{2 \cdot 11^{\frac{2}{2}} + 2 \sqrt{11} \cdot - 4 - 3 \sqrt{11} - 3 \cdot - 4}{- 5}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 \cdot 11^{\frac{2}{2}} + 2 \sqrt{11} \cdot - 4 - 3 \sqrt{11} - 3 \cdot - 4}{- 5}$

Rewrite the expression.

$\frac{2 \cdot 11^{1} + 2 \sqrt{11} \cdot - 4 - 3 \sqrt{11} - 3 \cdot - 4}{- 5}$

Evaluate the exponent.

$\frac{2 \cdot 11 + 2 \sqrt{11} \cdot - 4 - 3 \sqrt{11} - 3 \cdot - 4}{- 5}$

Multiply $2$ by $11$ .

$\frac{22 + 2 \sqrt{11} \cdot - 4 - 3 \sqrt{11} - 3 \cdot - 4}{- 5}$

Multiply $- 4$ by $2$ .

$\frac{22 - 8 \sqrt{11} - 3 \sqrt{11} - 3 \cdot - 4}{- 5}$

Multiply $- 3$ by $- 4$ .

$\frac{22 - 8 \sqrt{11} - 3 \sqrt{11} + 12}{- 5}$

Add $22$ and $12$ .

$\frac{34 - 8 \sqrt{11} - 3 \sqrt{11}}{- 5}$

Subtract $3 \sqrt{11}$ from $- 8 \sqrt{11}$ .

$\frac{34 - 11 \sqrt{11}}{- 5}$

Move the negative in front of the fraction.

$- \frac{34 - 11 \sqrt{11}}{5}$

The result can be shown in multiple forms.

Exact Form:

$- \frac{34 - 11 \sqrt{11}}{5}$

Decimal Form:

$0.49657453 \dots$

Simplify (2 square root of 11-3)/( square root of 11+4)

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