simplify the quotient: 3/sqrt7 - sqrt3

Answer 1

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)