00:01
For this problem, we have the function g of x equals 2x over x squared minus x.
00:05
Now, as we've seen in the previous similar problems, i'll be first trying to figure out how to rewrite our numerator of the limit definition of the derivative in a simplified form.
00:19
So we have g of x plus h would be 2x plus 2h divided by h squared plus 2xh plus x squared plus x squared minus x and then minus j.
00:32
G of x gives us minus 2x over x squared minus x.
00:38
So we can first get everything over a common denominator, writing this as 2x plus 2h times x squared minus x minus 2x times.
00:50
Now we'll write this in a simplified form for now.
00:53
So that would be minus 2x times x plus h all squared minus x minus h.
01:01
All over x squared minus x times x plus h all squared minus x minus h and one moment here so let's see here we now will have in the numerator after expanding everything out we come two x cubed plus two x squared h minus two x squared minus two h x squared minus two h x squared minus two h x x plus 2hx minus 2xh squared plus 2x squared minus 4h squared minus 2x squared minus 2x cubed all over x squared minus x times x plus all squared minus x minus h and we have then that we have 2x cubed minus 2x cubed plus, let's see here...