What is (2sqrt(5)+3)/(sqrt(5)-1) ?

The solution to (2sqrt(5)+3)/(sqrt(5)-1) is (13+5sqrt(5))/4

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simplify (2sqrt(5)+3)/(sqrt(5)-1)

simplify

\frac{2 5 + 3}{5 - 1}

\frac{13 + 5 5}{4}

Decimal Notation

6.04508 \dots

Solution steps

\frac{2 5 + 3}{5 - 1}

Multiply by the conjugate

\frac{5 + 1}{5 + 1}

= \frac{( 2 5 + 3 ) ( 5 + 1 )}{( 5 - 1 ) ( 5 + 1 )}

Expand

(25 + 3) (5 + 1) : 13 + 55

Expand

(5 - 1) (5 + 1) : 4

= \frac{13 + 5 5}{4}

(x + (2 + x^{2})) (x - (2 + x^{2}))

8 x - 6 (x - 4) - x

\frac{74}{5 - 7 i} + \frac{15 - 20 i}{1 - 2 i} - \frac{10 i}{2 - i}

\frac{2 + 2}{2}

I n^{1}

What is (2sqrt(5)+3)/(sqrt(5)-1) ?
The solution to (2sqrt(5)+3)/(sqrt(5)-1) is (13+5sqrt(5))/4