What is (7+sqrt(5))/(sqrt(5)-1) ?

The solution to (7+sqrt(5))/(sqrt(5)-1) is 2sqrt(5)+3

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simplify (7+sqrt(5))/(sqrt(5)-1)

simplify

\frac{7 + 5}{5 - 1}

25 + 3

Decimal Notation

7.47213 \dots

Solution steps

\frac{7 + 5}{5 - 1}

Multiply by the conjugate

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

= \frac{( 7 + 5 ) ( 5 + 1 )}{( 5 - 1 ) ( 5 + 1 )}

Expand

(7 + 5) (5 + 1) : 85 + 12

Expand

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

= \frac{8 5 + 12}{4}

Factor out common term

4 : 4 (25 + 3)

= \frac{4 ( 2 5 + 3 )}{4}

Cancel the common factor:

4

= 25 + 3

11 x^{2} - 78 x + 7

\frac{2 x}{1}

\frac{12}{14}

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

- 2 + \frac{9}{4}

What is (7+sqrt(5))/(sqrt(5)-1) ?
The solution to (7+sqrt(5))/(sqrt(5)-1) is 2sqrt(5)+3