00:01
In the given question we are told that we should find f of a and f of a plus h and the difference quotient of the following function.
00:13
The function given to us is f of x is equal to 2x divided by x minus 1.
00:22
So to find f of a what we should do is we should simply replace x with.
00:33
So when you do that you get f of a is equal to 2a divided by a minus 1.
00:43
Next up we are told to find f of a plus h.
00:48
So over here what you would do is you can simply replace again you can replace x with a plus h.
00:59
And in that case what you would have is f of a plus h is equal to 2 times a plus h divided by a plus h minus 1.
01:16
Which would then simplify as 2a plus 2h divided by a plus h minus 1.
01:25
Now finally we are told to find the difference quotient.
01:30
The difference quotient.
01:34
And we are told that the difference quotient can be found as f of a plus h minus f of a divided by h.
01:49
So since we have all these, already we have found all these, we can substitute for f of a plus h as 2 times a plus h.
02:01
Or let's just substitute as 2a plus 2h divided by a plus h minus 1.
02:11
So that is f of a plus h minus f of a which is 2a divided by a minus 1.
02:18
And then you have divided by h...