Question

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

Answer 1

See a solution process below:

Explanation:

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)`