What is 2/(sqrt(5)+\sqrt{3)} ?

The solution to 2/(sqrt(5)+\sqrt{3)} is sqrt(5)-sqrt(3)

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simplify 2/(sqrt(5)+\sqrt{3)}

simplify

\frac{2}{5 + 3}

5 - 3

Solution steps

\frac{2}{5 + 3}

Multiply by the conjugate

\frac{5 - 3}{5 - 3}

= \frac{2 ( 5 - 3 )}{( 5 + 3 ) ( 5 - 3 )}

Expand

2 (5 - 3) : 25 - 23

Expand

(5 + 3) (5 - 3) : 2

= \frac{2 5 - 2 3}{2}

Factor out common term

2

= \frac{2 ( 5 - 3 )}{2}

Cancel the common factor:

2

= 5 - 3

20 - 5

\frac{8 ( x - 4 )}{( x - 4 ) ^{2}}

\frac{3}{8} \div 5

cos (x) - cos^{2} (x)

What is 2/(sqrt(5)+\sqrt{3)} ?
The solution to 2/(sqrt(5)+\sqrt{3)} is sqrt(5)-sqrt(3)