What is (11)/(3sqrt(5)+1) ?

The solution to (11)/(3sqrt(5)+1) is (3sqrt(5)-1)/4

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simplify (11)/(3sqrt(5)+1)

simplify

\frac{11}{3 5 + 1}

\frac{3 5 - 1}{4}

Decimal Notation

1.42705 \dots

Solution steps

\frac{11}{3 5 + 1}

Multiply by the conjugate

\frac{3 5 - 1}{3 5 - 1}

= \frac{11 ( 3 5 - 1 )}{( 3 5 + 1 ) ( 3 5 - 1 )}

Expand

11 (35 - 1) : 335 - 11

Expand

(35 + 1) (35 - 1) : 44

= \frac{33 5 - 11}{44}

Factor out common term

11 : 11 (35 - 1)

= \frac{11 ( 3 5 - 1 )}{44}

Factor the number:

44 = 11 \cdot 4

= \frac{11 ( 3 5 - 1 )}{11 \cdot 4}

Cancel the common factor:

11

= \frac{3 5 - 1}{4}

\frac{1}{4} x^{2} + x^{2}

(3 y + 4) (2 y - 3)

\frac{26}{13}

ln ((x y)^{8})

12 \frac{5}{6} x - 14 x + \frac{1}{6} x