What is 1/(2+sqrt(3))+1/(2-sqrt(3)) ?

The solution to 1/(2+sqrt(3))+1/(2-sqrt(3)) is 4

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simplify 1/(2+sqrt(3))+1/(2-sqrt(3))

simplify

\frac{1}{2 + 3} + \frac{1}{2 - 3}

4

Solution steps

\frac{1}{2 + 3} + \frac{1}{2 - 3}

Least Common Multiplier of

2 + 3, 2 - 3 : (2 + 3) (2 - 3)

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

2 - 3 + 2 + 3 = 4

= \frac{4}{( 2 + 3 ) ( 2 - 3 )}

Apply Difference of Two Squares

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

= \frac{4}{1}

Divide the numbers:

\frac{4}{1} = 4

= 4

lo g_{\frac{1}{2}} (\frac{1}{5})

lo g_{3} (9^{2} \cdot 7^{4})

3 x^{2} + 51 x + 216

\frac{1}{3} \cdot \frac{3}{4}

25 \cdot 1 0^{- 3}

What is 1/(2+sqrt(3))+1/(2-sqrt(3)) ?
The solution to 1/(2+sqrt(3))+1/(2-sqrt(3)) is 4