Question

1%7D%2B%5Cdfrac%7B1%7D%7B%5Csqrt2-1%7D.%24" id="TexFormula1" title="Simplify $\dfrac{1}{\sqrt2+1}+\dfrac{1}{\sqrt2-1}.$" alt="Simplify $\dfrac{1}{\sqrt2+1}+\dfrac{1}{\sqrt2-1}.$" align="absmiddle" class="latex-formula">

Answer 1

Answer:

Step-by-step explanation:

common denominator

$(\sqrt(2)+1)(\sqrt(2)-1) = (\sqrt{2})^2-1^{2}=2-1 = 1$

Add with common denominator

$\dfrac{1}{\sqrt2+1}+\dfrac{1}{\sqrt2-1}.$

$= \frac{{\sqrt2-1}}{1} + \frac{\sqrt2+1}{1}$

$=2* (\sqrt2)$