How do you rationalize the denominator and simplify $\frac{5}{\sqrt{6} - 2}$ $5/(sqrt6-2)$ ?

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Answer 1 · 2018-08-05T03:59:52

I tried this:

Let us multiply and divide by $\sqrt{6} + 2$ $sqrt(6)+2$ :

$\frac{5}{\sqrt{6} - 2} \cdot \frac{\sqrt{6} + 2}{\sqrt{6} + 2}$ $5/(sqrt(6)-2)*color(red)((sqrt(6)+2)/(sqrt(6)+2))$

$= \frac{5 \sqrt{6} + 10}{6 - 4}$ $=(5sqrt(6) + 10)/(6-4)$

$= \frac{5 \sqrt{6} + 10}{2}$ $=(5 sqrt(6)+10)/2$

$= \frac{5}{2} \sqrt{6} + 5$ $=5/2sqrt(6)+5$

$= 5 (\frac{\sqrt{6}}{2} + 1)$ $=5(sqrt(6)/2+1)$

How do you rationalize the denominator and simplify 5/(sqrt6-2)5√6−25/(sqrt6-2)?