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

The solution to (3-2sqrt(5))/(sqrt(5)-1) is (sqrt(5)-7)/4

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

simplify

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

\frac{5 - 7}{4}

Decimal Notation

- 1.19098 \dots

Solution steps

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

Multiply by the conjugate

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

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

Expand

(3 - 25) (5 + 1) : 5 - 7

Expand

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

= \frac{5 - 7}{4}

\frac{6 x}{3 x - 2} - \frac{4}{3 x - 2}

(3 x^{2} - 2) (2 x + 4) - 2 x^{2} + 6 x + 7

72 + 98

- q^{2} - 9 q - 14

3 x^{10} + 6 x^{8} + 9 x^{6}

What is (3-2sqrt(5))/(sqrt(5)-1) ?
The solution to (3-2sqrt(5))/(sqrt(5)-1) is (sqrt(5)-7)/4