How do you simplify #3/(sqrt(3)-3)#?

Question

5449 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-02-15T10:15:06

Actually there is a much easier way to do this:

First i will rewrite this to ensure clarity:

#(sqrt3 * sqrt3)/(sqrt3 - sqrt3 * sqrt3)#

So now lets remove common factor

#(sqrt3 ( sqrt3))/( sqrt3(1-sqrt3))#

Now leta get rid of the # sqrt 3# in the denominator and numerator:

# ( sqrt3)/(1-sqrt3)#

Now we shall rationalize:

# ( sqrt3)/(1-sqrt3) * (1 + sqrt3) /(1 + sqrt3)#

That should be

#( sqrt3 + 3)/(1-3) = ( sqrt3 + 3)/-2 #