Simplify $\frac{3}{2 \sqrt 3 - 3}.$Simplify $(3)/(2 \sqrt 3 - 3).$

Question

Simplify $\frac{3}{2 \sqrt 3 - 3}.$
`Simplify $(3)/(2 \sqrt 3 - 3).$`

Answer 1

`2√(3)+3`

Explanation:

`$(3)/(2 \sqrt 3 - 3)$`

Rationalize the fraction.

`$(3)/(2 \sqrt 3 - 3)\cdot (2 \sqrt 3 + 3)/(2 \sqrt 3 + 3) =(6√(3)+9 )/(12-9) =(6√(3)+9 )/(3) =2√(3)+3 $`

Note that I used the positive signal because we would have a difference of squares.