Hello there. To solve this question, you will need to conclude what happens when you multiply the fraction by the factor sqrt(7)/sqrt(7), it is, rationalizing with this factor (instead of the conjugate of the denominator expression)
We'll get:
5/(1+sqrt(7)) * sqrt(7)/sqrt(7)
Apply the foil
5sqrt(7)/(sqrt(7) + 7)
As you can see, you wouldn't be able to find a neat expression to this.
The right way is: multiply the fraction by the conjugate of the denominator expression, it is (sqrt(7) - 1)/(sqrt(7) - 1)
5/(1+sqrt(7)) * (sqrt(7) - 1)/(sqrt(7) - 1)
Apply the foil and remember (a + b)(a - b) = a² - b²
(5sqrt(7) - 5)/(7 - 1)
(5sqrt(7) - 5)/6
This is the expression we would be looking for. Note that the rationalizing process refers to getting rid of the square root (to be fair, any kind of root) of the denominator.
First case: a square root on the denominator;
Second case: another type of root on the denominator;
Third case: a sum of terms involving a root of any type.
It follows the same process we did to solve the question, but sometimes we'll need to use one of the other cases.