How do you rationalize the denominator and simplify $\frac{2 \sqrt{5} - 3 \sqrt{2}}{2 \sqrt{5} + 3 \sqrt{2}}$ $[2sqrt(5) - 3sqrt(2)] / [2sqrt(5) + 3sqrt(2)]$ ?

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How do you rationalize the denominator and simplify $\frac{2 \sqrt{5} - 3 \sqrt{2}}{2 \sqrt{5} + 3 \sqrt{2}}$ $[2sqrt(5) - 3sqrt(2)] / [2sqrt(5) + 3sqrt(2)]$ ?

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Answer 1 · 2016-03-14T17:59:25

$19 - 3 \sqrt{10}$ $19 - 3sqrt10$

Explanation:

Multiply both numerator and denominator by $(2 \sqrt{5} - 3 \sqrt{2})$ $(2sqrt5 - 3sqrt2)$

$[\frac{2 \sqrt{5} - 3 \sqrt{2}}{2 \sqrt{5} + 3 \sqrt{2}}] [\frac{2 \sqrt{5} - 3 \sqrt{2}}{2 \sqrt{5} - 3 \sqrt{2}}] = \frac{{(2 \sqrt{5} - 3 \sqrt{2})}^{2}}{20 - 18} = \frac{20 + 18 - 6 \sqrt{10}}{2} =$ $[(2sqrt5- 3sqrt2)/(2sqrt5 + 3sqrt2)][(2sqrt5 - 3sqrt2)/(2sqrt5 - 3sqrt2)] =(2sqrt5 - 3sqrt2)^2/(20 - 18) = (20 + 18 - 6sqrt10)/2 =$
$= 19 - 3 \sqrt{10}$ $= 19 - 3sqrt10$

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How do you rationalize the denominator and simplify $\frac{2 \sqrt{5} - 3 \sqrt{2}}{2 \sqrt{5} + 3 \sqrt{2}}$ $[2sqrt(5) - 3sqrt(2)] / [2sqrt(5) + 3sqrt(2)]$ ?

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How do you rationalize the denominator and simplify $\frac{2 \sqrt{5} - 3 \sqrt{2}}{2 \sqrt{5} + 3 \sqrt{2}}$ $[2sqrt(5) - 3sqrt(2)] / [2sqrt(5) + 3sqrt(2)]$ ?