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

The solution to (sqrt(5)-sqrt(3))/(sqrt(5)+\sqrt{3)} is 4-sqrt(15)

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

simplify

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

4 - 15

Decimal Notation

0.12701 \dots

Solution steps

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

Multiply by the conjugate

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

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

Expand

(5 - 3) (5 - 3) : 8 - 215

Expand

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

= \frac{8 - 2 15}{2}

Factor out common term

2 : 2 (4 - 15)

= \frac{2 ( 4 - 15 )}{2}

Cancel the common factor:

2

= 4 - 15

(s^{- 2} t^{2})^{2}

2010 \cdot (- 52)

\frac{3}{5} + \frac{2}{7}

3 m - 7 m + 2 m

72 z^{5}

What is (sqrt(5)-sqrt(3))/(sqrt(5)+\sqrt{3)} ?
The solution to (sqrt(5)-sqrt(3))/(sqrt(5)+\sqrt{3)} is 4-sqrt(15)