Simplify this term

Let's work on numerator first    expand

3sqrt5 - 6 +5 -2sqrt5 = sqrt5 -1

so you have  ( sqrt5-1)  / ( 5-sqrt5)   now multiply and expand by  (5+sqrt5)/(5+sqrt5)=

(5sqrt5 +5 -5 -sqrt5 ) /  (25 + 5 sqrt5-5sqrt5 -5)     Simplify by collecting like terms

4sqrt5 / 20        and now, simplify the fraction

sqrt5 / 5

Simplify the following:
((3 + sqrt(5)) (sqrt(5) - 2))/(5 - sqrt(5))

(3 + sqrt(5)) (sqrt(5) - 2) = 3 (-2) + 3 sqrt(5) + sqrt(5) (-2) + sqrt(5) sqrt(5) = -6 + 3 sqrt(5) - 2 sqrt(5) + 5 = sqrt(5) - 1:
(sqrt(5) - 1)/(5 - sqrt(5))

Multiply numerator and denominator of (sqrt(5) - 1)/(5 - sqrt(5)) by 5 + sqrt(5):
((sqrt(5) - 1) (5 + sqrt(5)))/((5 - sqrt(5)) (5 + sqrt(5)))

(5 - sqrt(5)) (5 + sqrt(5)) = 5×5 + 5 sqrt(5) - sqrt(5)×5 - sqrt(5) sqrt(5) = 25 + 5 sqrt(5) - 5 sqrt(5) - 5 = 20:
((sqrt(5) - 1) (5 + sqrt(5)))/(20)

(sqrt(5) - 1) (5 + sqrt(5)) = -5 - sqrt(5) + sqrt(5)×5 + sqrt(5) sqrt(5) = -5 - sqrt(5) + 5 sqrt(5) + 5 = 4 sqrt(5):
(4 sqrt(5))/(20)

4/20 = 4/(4×5) = 1/5:
Answer: |(sqrt(5))/(5)

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

I know the answer is    sqrt (5) / 5

\(\frac{(3+\sqrt 5)(\sqrt 5-2)}{5-\sqrt 5}\)

\(=\frac{3\sqrt 5-6+5-2\sqrt5}{5-\sqrt5}\)          expand to the 3rd Binom

\(=\frac{\sqrt5-1}{5-\sqrt5}\times \frac{5+\sqrt5}{5+\sqrt5}\)        \(\frac{multiply}{3rdBinom}\)

\(=\frac{5\sqrt5+5-5-\sqrt5}{25-5}\)           add, subtract

\(=\frac{4\sqrt5}{20}\)                           shortened

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