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

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Answer 1 · 2015-12-02T16:00:29

$(2sqrt5)/5-1$

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:

$(2sqrt5-5)/5$

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