Question

Simplify 1+√2÷√5+√3+1-√2÷√5-√3

Answer 1

Answer:

Step-by-step explanation:

1+(√2/√5)+√3+1-(√2/√3)-√3

1+1+(√2/√5)-(√2/√3)

2/1+√2/√5-√2/√3

Take LCM of √5,√3 and 1

It's √15

(2√15+√6-√10)/√15

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Answer 2

$\frac{1+\sqrt2}{\sqrt5+\sqrt3}+\frac{1-\sqrt2}{\sqrt5-\sqrt3}=\sqrt{5}-\sqrt{6}$

Step-by-step explanation:

Given : Expression $\frac{1+\sqrt2}{\sqrt5+\sqrt3}+\frac{1-\sqrt2}{\sqrt5-\sqrt3}$

To find : Simplify the expression ?

Solution :

$\frac{1+\sqrt2}{\sqrt5+\sqrt3}+\frac{1-\sqrt2}{\sqrt5-\sqrt3}$

Taking Least common denominator,

$=\frac{(1+\sqrt2)(\sqrt5-\sqrt3)+(1-\sqrt2)(\sqrt5+\sqrt3)}{(\sqrt5+\sqrt3)(\sqrt5-\sqrt3)}$

$=\frac{\sqrt{5}-\sqrt3+\sqrt{10}-\sqrt{6}+\sqrt5+\sqrt3-\sqrt{10}-\sqrt{6}}{(\sqrt5)^2-(\sqrt3)^2}$

$=\frac{2\sqrt{5}-2\sqrt{6}}{5-3}$

$=\frac{2(\sqrt{5}-\sqrt{6})}{2}$

$=\sqrt{5}-\sqrt{6}$

Therefore, $\frac{1+\sqrt2}{\sqrt5+\sqrt3}+\frac{1-\sqrt2}{\sqrt5-\sqrt3}=\sqrt{5}-\sqrt{6}$

#Learn more

Simplify =1/√5+√3 + 1/2(√5-√3)

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