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

7.87298 \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

2 n + 6

- 8 (x + 9) = 2 (x + 4)

x^{2} - 3 x - 4 = 0

\frac{1}{2} (1)^{3}

3 x^{2} + 4 x + 7 = 0

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)