Question

Help me with this question
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Answer 1

Answer:

8

Step-by-step explanation:

Given,

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

Taking lcm,

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

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

as we know that, (a+b)²+(a-b)²=2(a²+b²)

$= \frac{2 \times 8}{2}$

$= 8$