Question

Find the difference. express your answer in simplest form. (2s/s^2-4s+4) - (4/s^2-4s+4)

Answer 1

To find the difference, we are going to destroy the parenthesis first, and then, we are going to perform the operations. Remember that to destroy a parenthesis preceded by a negative sign (-), you should change the signs of the factors inside the parenthesis:
$\frac{2s}{s^2-4s+4} -( \frac{4}{s^2-4s+4} )$
$\frac{2s}{s^2-4s+4} -\frac{4}{s^2-4s+4}= \frac{2s-4}{s^2-4s+4}$

Now we can factor both numerator and denominator and simplify:
$\frac{2s-4}{s^2-4s+4} = \frac{2(s-2)}{(s-2)^2} = \frac{2}{s-2}$

We can conclude that the difference in simplest form is: $\frac{2}{s-2}$

Answer 2

To get started, combine -4s+4 with 4s - 4.  Result:  0.  That leaves

 2s        4          2(s+2)
------ - ------- = ------------
s^2      s^2           s^2