Question

rationalize the denominator of..
$3 - \sqrt{5} \div 3 + \sqrt{5}$
step by step..


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Answer 1

Answer:

Step-by-step explanation:

$\frac{3-\sqrt{5} }{3+\sqrt{5} }$

$\\\frac{3-\sqrt{5} }{3+\sqrt{5} }$ * $\\\frac{3-\sqrt{5} }{3-\sqrt{5} }$

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

$\frac{9+5-6\sqrt{5} }{9-5}$

$\frac{14-6\sqrt{5} }{4}$

$\frac{7-3\sqrt{5} }{2}$

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Answer 2

$\large{ \underline{ \bf{question}}}$

Rationalize the denominator of

$\tt \: \frac{3 - \sqrt{5} }{3 + \sqrt{5} }$

Step by step.

$\large{ \underline{ \bf{answer}}}$

We have,

$\tt \color{brown} \frac{3 - \sqrt{5} }{3 + \sqrt{5} }$

Multiplying by (3 - √5) in both Numerator and denominator

$\tt \color{brown} \frac{3 - \sqrt{5} }{3 + \sqrt{5} } \times \frac{3 - \sqrt{5} }{3 - \sqrt{5} }$

Using algebraic identities

$\small {\bf \: (x + y)(x - y) = {x}^{2} - {y}^{2} }$

and

$\small{ \bf {(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy}$

we will get,

$\tt \color{brown} \frac{ {3}^{2} + { {( \sqrt{5}) }^{2} + 2(3)( \sqrt{5} ) } }{ {3}^{2} - {( \sqrt{5}) }^{2} } \\ \\ \tt \color{brown} \frac{9 + 5 + 6 \sqrt{5} }{9 - 5} \\ \\ \tt \color{brown} \frac{14 + 6 \sqrt{5} }{4}$

Taking 2 common in numerator and also in denominator

$\tt \color{brown} \frac{2(7 + 3 \sqrt{5} )}{2(2)} \\ \\ \tt \color{brown} \frac{ 7 + 3 \sqrt{5} }{2}$

(Ans.)