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

The solution to (3+sqrt(5))/(sqrt(5)+4) is (sqrt(5)+7)/(11)

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simplify (3+sqrt(5))/(sqrt(5)+4)

simplify

\frac{3 + 5}{5 + 4}

\frac{5 + 7}{11}

Decimal Notation

0.83964 \dots

Solution steps

\frac{3 + 5}{5 + 4}

Multiply by the conjugate

\frac{5 - 4}{5 - 4}

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

Expand

(3 + 5) (5 - 4) : - 5 - 7

Expand

(5 + 4) (5 - 4) : - 11

= \frac{- 5 - 7}{- 11}

\frac{- 5 - 7}{- 11} = \frac{5 + 7}{11}

= \frac{5 + 7}{11}

x^{- 4} y

\frac{9}{4} \div \frac{3}{8}

x^{- 6} y

(- \frac{x}{2 y})^{2}

x^{3} - x^{2} y - x y^{2} + y^{3}

What is (3+sqrt(5))/(sqrt(5)+4) ?
The solution to (3+sqrt(5))/(sqrt(5)+4) is (sqrt(5)+7)/(11)