Question

how does one simplify (3+sqrt(3))/(3-sqrt(3)) to 2+sqrt(3)?

Answer 1

To simplify this fraction,

\( \dfrac{3+\sqrt{3} }{3- \sqrt{3}} \)

multiply it by

\( \dfrac{3+\sqrt{3} }{3+ \sqrt{3}} \)

Answer 2

In general, if you have a fraction with denominator
\(a + \sqrt{b} \),
and you need to rationalize the fraction, multiply the fraction by
\( \dfrac{a - \sqrt{b} }{a - \sqrt{b}} \)

This works because
\( (a + \sqrt{b})(a - \sqrt{b}) \)
\( = a^2 - (\sqrt{b})^2 \)
\(= a^2 - b\)
If a and b are rational, then \( a^2 - b\) is also rational.

Answer 3

Got it, thanks!

Answer 4

wlcm