What is expand (4/((3-sqrt(5))^2))^2 ?

The solution to expand (4/((3-sqrt(5))^2))^2 is 47/2+(21sqrt(5))/2

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expand (4/((3-sqrt(5))^2))^2

expand

(\frac{4}{( 3 - 5 ) ^{2}})^{2}

\frac{47}{2} + \frac{21 5}{2}

Solution steps

(\frac{4}{( 3 - 5 ) ^{2}})^{2}

\frac{4}{( 3 - 5 ) ^{2}} = \frac{2}{7 - 3 5}

= (\frac{2}{7 - 3 5})^{2}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{2 ^{2}}{( 7 - 3 5 ) ^{2}}

(7 - 35)^{2} = 94 - 425

= \frac{2 ^{2}}{94 - 42 5}

Factor

94 - 425 : 2 (47 - 215)

= \frac{2 ^{2}}{2 ( 47 - 21 5 )}

Cancel the common factor:

2

= \frac{2}{47 - 21 5}

Rationalize

\frac{2}{47 - 21 5} : \frac{47 + 21 5}{2}

= \frac{47 + 21 5}{2}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{47 + 21 5}{2} = \frac{47}{2} + \frac{21 5}{2}

= \frac{47}{2} + \frac{21 5}{2}

l im x \Rightarrow 5 (3 x^{2} + x - 2)

\frac{( 2 s + 2 + s e ^{- s - 1} )}{s ( s + 1 ) ^{2}}

\frac{- 2 x - 9}{( x - 2 ) ( x - 4 ) ( x + 3 )}

\frac{x ^{2} + 2 x + 4}{( x + 1 ) ^{3}}

(4 d + 3 e - 8 f) - (- 3 d +, - 5 f + 6)

What is expand (4/((3-sqrt(5))^2))^2 ?
The solution to expand (4/((3-sqrt(5))^2))^2 is 47/2+(21sqrt(5))/2