How do you simplify $\frac{\sqrt{5} + 2}{\sqrt{5}} - 2)$ $(sqrt5+2)/sqrt5-2)$ ?

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How do you simplify $\frac{\sqrt{5} + 2}{\sqrt{5}} - 2)$ $(sqrt5+2)/sqrt5-2)$ ?

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Answer 1 · 2015-12-02T16:00:29

$\frac{2 \sqrt{5}}{5} - 1$ $(2sqrt5)/5-1$

Explanation:

Simplify $\frac{\sqrt{5} + 2}{\sqrt{5}}$ $(sqrt5+2)/sqrt5$ .

$\frac{\sqrt{5} + 2}{\sqrt{5}} (\frac{\sqrt{5}}{\sqrt{5}}) = \frac{{(\sqrt{5})}^{2} + 2 \sqrt{5}}{{(\sqrt{5})}^{2}} = \frac{5 + 2 \sqrt{5}}{5} = 1 + \frac{2 \sqrt{5}}{5}$ $(sqrt5+2)/sqrt5(sqrt5/sqrt5)=((sqrt5)^2+2sqrt5)/(sqrt5)^2=(5+2sqrt5)/5=1+(2sqrt5)/5$

Therefore, when we add that to the original expression:

$(1 + \frac{2 \sqrt{5}}{5}) - 2 = \frac{2 \sqrt{5}}{5} - 1$ $(1+(2sqrt5)/5)-2=color(blue)((2sqrt5)/5-1$

This can also be written as:

$\frac{2 \sqrt{5} - 5}{5}$ $(2sqrt5-5)/5$

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How do you simplify $\frac{\sqrt{5} + 2}{\sqrt{5}} - 2)$ $(sqrt5+2)/sqrt5-2)$ ?

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