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

5.23606 \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

- x^{2} + 12 x

- 3 + 15

\frac{1}{0} - \frac{1}{0}

\frac{b ^{2} - 64}{8 - b}

- 4 + 16