How do you simplify $\frac{\sqrt{5} + 3}{4 - \sqrt{5}}$ $(sqrt5+3)/(4-sqrt5)$ ?

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How do you simplify $\frac{\sqrt{5} + 3}{4 - \sqrt{5}}$ $(sqrt5+3)/(4-sqrt5)$ ?

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Answer 1 · 2016-09-20T16:36:04

$\frac{17}{11} + \frac{7 \sqrt{5}}{11}$ $17/11 + [7sqrt5]/11$

Explanation:

$\frac{\sqrt{5} + 3}{4 - \sqrt{5}} = \frac{\sqrt{5} + 3}{4 - \sqrt{5}} \cdot \frac{4 + \sqrt{5}}{4 + \sqrt{5}} = \frac{4 \sqrt{5} + 12 + 5 + 3 \sqrt{5}}{16 - 5} = \frac{17 + 7 \sqrt{5}}{11} = \frac{17}{11} + \frac{7 \sqrt{5}}{11}$ $[sqrt5 + 3]/[4 - sqrt5] = [sqrt5 + 3]/[4 - sqrt5] * [4 + sqrt5]/[4 + sqrt5] = [4sqrt5 + 12 + 5 + 3sqrt5]/[16 - 5]=[17 + 7sqrt5]/11 = 17/11 +[ 7sqrt5]/11$

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How do you simplify $\frac{\sqrt{5} + 3}{4 - \sqrt{5}}$ $(sqrt5+3)/(4-sqrt5)$ ?

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