What is (sqrt(11)+sqrt(3))/(sqrt(11)-\sqrt{3)} ?

The solution to (sqrt(11)+sqrt(3))/(sqrt(11)-\sqrt{3)} is (7+sqrt(33))/4

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simplify (sqrt(11)+sqrt(3))/(sqrt(11)-\sqrt{3)}

simplify

\frac{11 + 3}{11 - 3}

\frac{7 + 33}{4}

Decimal Notation

3.18614 \dots

Solution steps

\frac{11 + 3}{11 - 3}

Multiply by the conjugate

\frac{11 + 3}{11 + 3}

= \frac{( 11 + 3 ) ( 11 + 3 )}{( 11 - 3 ) ( 11 + 3 )}

Expand

(11 + 3) (11 + 3) : 14 + 233

Expand

(11 - 3) (11 + 3) : 8

= \frac{14 + 2 33}{8}

Factor out common term

2 : 2 (7 + 33)

= \frac{2 ( 7 + 33 )}{8}

Factor the number:

8 = 2 \cdot 4

= \frac{2 ( 7 + 33 )}{2 \cdot 4}

Cancel the common factor:

2

= \frac{7 + 33}{4}

x^{4} + 16 x^{2}

x^{3} - 4 x^{2} + 5 x

2 x^{2} + 8 x + 77 = 0

k^{2} + 7 k + 6

k^{2} + 4 k - 5 = 0

What is (sqrt(11)+sqrt(3))/(sqrt(11)-\sqrt{3)} ?
The solution to (sqrt(11)+sqrt(3))/(sqrt(11)-\sqrt{3)} is (7+sqrt(33))/4