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

0.31385 \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}

7 r + 14 s

(4 a b^{2} + 2 c) (- 2 a b^{2} + c)

\frac{( 4 w ^{- 1} c ^{4} ) ^{- 5}}{5 c ^{- 3}}

1 - \frac{4}{9} a^{8}

\frac{9}{2} - \frac{7}{16}

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