What is 4/(3+sqrt(5)) ?

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

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simplify 4/(3+sqrt(5))

simplify

\frac{4}{3 + 5}

3 - 5

Decimal Notation

0.76393 \dots

Solution steps

\frac{4}{3 + 5}

Multiply by the conjugate

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

= \frac{4 ( 3 - 5 )}{( 3 + 5 ) ( 3 - 5 )}

Expand

4 (3 - 5) : 12 - 45

Expand

(3 + 5) (3 - 5) : 4

= \frac{12 - 4 5}{4}

Factor out common term

4 : 4 (3 - 5)

= \frac{4 ( 3 - 5 )}{4}

Cancel the common factor:

4

= 3 - 5

3 (x - 5)^{2} - 3 (2 x - 1)

\frac{2}{k + 3} + \frac{1}{k - 1}

6 \cdot \frac{5}{4}

12 x^{3} - 56 x^{2} + 87 x - 45

\frac{2}{sin ( x )}