Question

simplify: the following in the picture
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Answer 1

Hii mate,

✔✔✔SOLUTION...

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Answer 2

$\Large \textsc{Identities Used...} \\ \\ \\ \\ 1.\ \ \displaystyle \frac{a}{b}+\frac{b}{a} = \frac{a^2+b^2}{ab} \\ \\ \\ 2.\ \ (a+b)^2+(a-b)^2=2(a^2+b^2) \\ \\ \\ 3.\ \ (a-b)(a+b)=a^2-b^2$

$\displaystyle \Longrightarrow\ \frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}+\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}} \\ \\ \\ \Longrightarrow\ \frac{(\sqrt{5}+\sqrt{3})^2+(\sqrt{5}-\sqrt{3})^2}{(\sqrt{5}-\sqrt{3})(\sqrt{5}+\sqrt{3})} \\ \\ \\ \Longrightarrow\ \frac{2((\sqrt{5})^2+(\sqrt{3})^2)}{(\sqrt{5})^2-(\sqrt{3})^2} \\ \\ \\ \Longrightarrow\ \frac{2(5+3)}{5-3} \\ \\ \\ \Longrightarrow\ \frac{2 \times 8}{2} \\ \\ \\ \Longrightarrow\ \bold{8}$

$\therefore\ \ \displaystyle \frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}+\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}} \ = \ \bold{8}$

$\huge\textit{\underline{\underline{Hence simplified!!!}}}$