Question

Rationalize the denominator and simplify: (\sqrt(b))/(\sqrt(b-3))

A. - 1/3
B. b+3sqrtb/b-9
C. b+3/b-9
D. 4sqrtb/b-9

Answer 1

To rationalize the denominator, we need to multiply the numerator and denominator by the conjugate of the denominator (in this case, the conjugate is sqrt(b) + sqrt(b-3)):

(sqrt(b))/(sqrt(b-3)) * (sqrt(b) + sqrt(b-3))/(sqrt(b) + sqrt(b-3))

After multiplying, we get:

= (sqrt(b) * sqrt(b) + sqrt(b) * sqrt(b-3)) / (b - 3)

= (b + sqrt(b(b-3))) / (b - 3)

Therefore, the simplified expression after rationalizing the denominator is:

(b + sqrt(b(b-3))) / (b - 3)

So, the correct answer is D. 4sqrtb/b-9.