Question

simplify √5+√3/√5–√3+√5–√3/√5+√3

Answer 1

Answer:

$\red { \frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}+\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}}\green { = 8}$

Step-by-step explanation:

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

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

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

$\boxed { \pink { (a+b)^{2}+(a-b)^{2} = 2(a^{2}+b^{2})}}$

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

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

$\green { = 8}$

Therefore.,

$\red { \frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}+\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}}\green { = 8}$

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Answer 2

Answer:

√5+√3/√5-√3 +√5-√3/√5+√3 =8