Simplify $\dfrac{1}{\sqrt2+1}+\dfrac{1}{\sqrt2-1}.$Simplify $(1)/(\sqrt2+1)+(1)/(\sqrt2-1).$

Question

Simplify $\dfrac{1}{\sqrt2+1}+\dfrac{1}{\sqrt2-1}.$
`Simplify $(1)/(\sqrt2+1)+(1)/(\sqrt2-1).$`

Answer 1

Explanation:

common denominator

`(\sqrt(2)+1)(\sqrt(2)-1) = (√(2))^2-1^(2)=2-1 = 1`

Add with common denominator

`(1)/(\sqrt2+1)+(1)/(\sqrt2-1).`

`= \frac{{\sqrt2-1}}{1} + (\sqrt2+1)/(1)`

`=2* (\sqrt2)`