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

1 Answer

Dec 2, 2015

#(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#

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