How do you simplify #5/(-5-3sqrt3)#?

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↳Redirected from "An electron in a hydrogen atom drops from energy level n=5 to n=3. What is the energy transition using the Rydberg equation?"

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Answer 1 · 2017-06-22T02:07:37

See a solution process below:

To simplify the expression we need to rationalize the denominator:

#5/(-5 - 3sqrt(3)) xx (-5 + 3sqrt(3))/(-5 + 3sqrt(3)) => (-25 + 15sqrt(3))/(25 - 15sqrt(3) + 15 sqrt(3) - 9(sqrt(3))^2) =>#

#(-25 + 15sqrt(3))/(25 - 0 - (9 * 3)) => (-25 + 15sqrt(3))/(25 - 27) =>#

#(-25 + 15sqrt(3))/-2#

Or

#25/2 - 15/2sqrt(3)#