What is 1/(sqrt(2)+1)+1/(sqrt(2)-1) ?

The solution to 1/(sqrt(2)+1)+1/(sqrt(2)-1) is 2sqrt(2)

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simplify 1/(sqrt(2)+1)+1/(sqrt(2)-1)

simplify

\frac{1}{2 + 1} + \frac{1}{2 - 1}

22

Decimal Notation

2.82842 \dots

Solution steps

\frac{1}{2 + 1} + \frac{1}{2 - 1}

Least Common Multiplier of

2 + 1, 2 - 1 : (1 + 2) (2 - 1)

Adjust Fractions based on the LCM

= \frac{2 - 1}{( 1 + 2 ) ( 2 - 1 )} + \frac{1 + 2}{( 1 + 2 ) ( 2 - 1 )}

Apply the fraction rule:

\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}

= \frac{2 - 1 + 1 + 2}{( 1 + 2 ) ( 2 - 1 )}

2 - 1 + 1 + 2 = 22

= \frac{2 2}{( 1 + 2 ) ( 2 - 1 )}

Apply Difference of Two Squares

(1 + 2) (2 - 1) : 1

= \frac{2 2}{1}

Apply the fraction rule:

\frac{a}{1} = a

= 22

y^{2} - 5 y - 9 = 0

9 m^{2} - 25 mn - 6 n^{2}

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- 16 x^{2} + 24 x + 240

8 x^{3} + 8 x y^{2} - 98 x

What is 1/(sqrt(2)+1)+1/(sqrt(2)-1) ?
The solution to 1/(sqrt(2)+1)+1/(sqrt(2)-1) is 2sqrt(2)