Rationalize the denominator and simplify: (\sqrt(b))/(\sqrt(b-3))
To rationalize the denominator, we need to multiply both the numerator and denominator by the conjugate of the denominator, which is \sqrt(b+3).
(\sqrt(b))/(\sqrt(b-3)) * (\sqrt(b+3))/(\sqrt(b+3))
This gives us:
= (\sqrt(b)*(sqrt(b+3)))/((\sqrt(b-3))*(\sqrt(b+3)))
= (sqrt(b)*(sqrt(b+3)))/(sqrt(b*b-3*3))
= (sqrt(b)*(sqrt(b+3)))/(sqrt(b^2-9))
= (sqrt(b*(b+3)))/(sqrt(b^2-9))
= sqrt(b^2+3b)/(sqrt((b+3)(b-3)))
Therefore, (\sqrt(b))/(\sqrt(b-3)) can be simplified to sqrt(b^2+3b)/(sqrt((b+3)(b-3))).