To rationalize the expression 5 ÷ (2 − √3), we need to eliminate the square root in the denominator.
We can do this by multiplying both the numerator and denominator by the conjugate of the denominator, which is 2 + √3. This is because when we multiply the conjugate of the denominator by the original denominator, we get a difference of squares that simplifies the expression:
5 ÷ (2 − √3) * (2 + √3) / (2 + √3)
Simplifying the numerator by multiplying the terms inside the brackets, we get:
5(2 + √3) / (2^2 - (√3)^2)
Simplifying further, we get:
5(2 + √3) / (4 - 3)
5(2 + √3) / 1
Therefore, the rationalized form of the expression is 5(2 + √3), which is equivalent to option C.