simplify the quotient: 3/sqrt7 - sqrt3
To simplify this quotient, we need to rationalize the denominator.
To do this, we will multiply both the numerator and denominator by the conjugate of the denominator:
(3/sqrt7 - sqrt3) * (sqrt7 + sqrt3) / (sqrt7 + sqrt3)
Expanding the numerator:
(3sqrt7 + 3sqrt3 - 7) / (sqrt7 + sqrt3)
Now we can simplify by dividing each term in the numerator by the denominator:
(3sqrt7 + 3sqrt3 - 7) / (sqrt7 + sqrt3)
= 3 - (4/sqrt7 + sqrt3)
So the simplified quotient is:
3 - (4/sqrt7 + sqrt3)