How do you simplify $\frac{2 + \sqrt{3}}{2 - \sqrt{3}}$ $(2+sqrt3)/(2-sqrt3)$ ?

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Answer 1 · 2015-03-30T12:24:30

Multiply both numerator and denominator of the fraction by the conjugate of the denominator to clear the square root from the denominator.

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

$= \frac{2 + \sqrt{3}}{2 - \sqrt{3}} \cdot \frac{2 + \sqrt{3}}{2 + \sqrt{3}}$ $=(2+sqrt(3))/(2-sqrt(3)) *(2+sqrt(3))/(2+sqrt(3))$

$= \frac{4 + 4 \sqrt{3} + 3}{4 - 3}$ $=(4+4sqrt(3)+3)/(4-3)$

$= 7 + 4 \sqrt{3}$ $= 7+4sqrt(3)$

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