Question

How do you simplify `(sqrt5+2)/sqrt5-2)`?

Answer 1

`(2sqrt5)/5-1`

Explanation:

Simplify `(sqrt5+2)/sqrt5`.

`(sqrt5+2)/sqrt5(sqrt5/sqrt5)=((sqrt5)^2+2sqrt5)/(sqrt5)^2=(5+2sqrt5)/5=1+(2sqrt5)/5`

Therefore, when we add that to the original expression:

`(1+(2sqrt5)/5)-2=color(blue)((2sqrt5)/5-1`

This can also be written as:

`(2sqrt5-5)/5`