help with rationalizing?

Question

Given the expression (h-4)/(sqroot of h - 2)
simply by ratinalization and simplify, evaluate the expression for h=4.

i dont understand. can some one help.

Answer 1

is the bottom
sqrt (h - 2)

or

(sqrt h) - 2

*********
I'll assume it's sqrt (h - 2)

To rationalize, you multiply the top and bottom of the fraction by the denominator. (That way, the square root is eliminated in the denominator.)

(h - 4) / sqrt(h - 2)
= (h - 4)(sqrt (h-2)) / (sqrt (h-2))(sqrt (h-2))
= (h - 4)(sqrt (h - 2)) / (h - 2)

Then to evaluate at h = 4, just plug in the value:

(4 - 4)(sqrt (4-2)) / (4 - 2)
= (0)(sqrt 2) / (2)
= 0

Answer 2

you can get rid of the sqrt( h - 2) by multiplying with sqrt( h - 2)/sqrt( h - 2); but personally i would leave the expression as it is now.

if you want to evaluate for h= -4 you should be able to handle complex numbers since you will get sqrt(-2). = i*sqrt(2)