What is 1/(sqrt(3)+1)+1/(sqrt(3)-1) ?

The solution to 1/(sqrt(3)+1)+1/(sqrt(3)-1) is square root of 3

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simplify 1/(sqrt(3)+1)+1/(sqrt(3)-1)

simplify

\frac{1}{3 + 1} + \frac{1}{3 - 1}

3

Decimal Notation

1.73205 \dots

Solution steps

\frac{1}{3 + 1} + \frac{1}{3 - 1}

Least Common Multiplier of

3 + 1, 3 - 1 : (1 + 3) (3 - 1)

Adjust Fractions based on the LCM

= \frac{3 - 1}{( 1 + 3 ) ( 3 - 1 )} + \frac{1 + 3}{( 1 + 3 ) ( 3 - 1 )}

Apply the fraction rule:

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

= \frac{3 - 1 + 1 + 3}{( 1 + 3 ) ( 3 - 1 )}

3 - 1 + 1 + 3 = 23

= \frac{2 3}{( 1 + 3 ) ( 3 - 1 )}

Apply Difference of Two Squares

(1 + 3) (3 - 1) : 2

= \frac{2 3}{2}

Cancel the common factor:

2

= 3

3 c^{2} + 10 c + 8

x^{2} - 13 x + 15 = 0

x^{2} - 2 x - 3 = 0

5 x^{2} = 25

- 4 x^{4} + 16 x^{3} + 128 x^{2}

What is 1/(sqrt(3)+1)+1/(sqrt(3)-1) ?
The solution to 1/(sqrt(3)+1)+1/(sqrt(3)-1) is square root of 3