Having trouble understanding this limit calculation

Question

Can anyone explain what is happening here? http://imgur.com/hn0UVjn ; I understand multiplying by the conjugate, but why do the signs change in the outlined part? And if the bottom denominator is being multiplied by the top denominator shouldn't the resulting numerator just be 1-1 instead of sqrt(4)-(sqrt(4+h)?

Answer 1

It has to do with the step ABOVE. Several operations are done at the same time with being written - typical of textbooks.

 

So look at the numerator of the fraction in the second line:

 

1 / (√(4 + h)) - 1 / √4               Add using the common denominator:

 

The numerator becomes (sorry about the inadequacies of this site):

 

√4 - (√(4 + h))    and the denominator becomes

 

(√4)(√(4 + h))     Now this fraction is divided by "h" giving the term in the box

 

OK?