## anonymous one year ago find the difference quotient of f(x)= (2x)/(x-1)

1. anonymous

2. Nnesha

we need to use formula f(x+h)-f(x) over h right ?

3. anonymous

instead of x im using a but yes

4. anonymous

f(a)= (2a)/(a-1)

5. Nnesha

ohh okay so first we have to find f(a+h) substitute a for a+h

6. anonymous

and f(a+h)= (2a+2h)/(-a-h)

7. anonymous

am i correct

8. Nnesha

the denominator would be a-1 = (a+h)-1 so it would be a+h-1 it's not a multiplication

9. anonymous

oh alright

10. Nnesha

alright so now we can substitute f(a+h) for that into the formula $\huge \rm \frac{ \frac{ 2a+2h }{ a+h-1 } +\frac{ 2a }{ a-1 } }{ h }$ now find the common denominator

11. anonymous

so you multiply it by h?

12. Nnesha

first deal with the numerator 2a+2h/a+h-1 + 2a/a-1

13. anonymous

14. Nnesha

what would be the common denominator ?

15. Nnesha

brb i'll login to other laptop

16. anonymous

shouldnt it be a+h-1?

17. Nnesha

both denominator are not the same so we should multiply both denominator $\huge\rm \frac{ (\color{Red}{a-1})(2a+2h) + 2a(\color{blue}{a+h-1}) }{ (a+h-1)(a-1)}$ and when we find common denominator we should multiply numerator of first fraction by the denominator of 2nd fraction

18. Nnesha

and multiply the numerator of 2nd fraction with the denominator of first

19. anonymous

so what did get

20. Nnesha

|dw:1443222925608:dw| kinda like cross multiplication

21. Nnesha

now distribute

22. anonymous

ok one sec

23. anonymous

is a+1 conssidered one term?

24. Nnesha

no term is separated by + or minus sign so two terms

25. anonymous

okay i got it

26. anonymous

|dw:1443223280971:dw|

27. anonymous

am i correct

28. Nnesha

wait a sec

29. Nnesha

|dw:1443223535245:dw| that supposed to be -2a bec 2a times -1 = -2a :=)

30. Nnesha

now combine like terms

31. Nnesha

|dw:1443223669791:dw|

32. anonymous

okay

33. anonymous

we usually cancel terms out did i miss a minus symbol somewhere

34. Nnesha

ye .. there is a negative sign in the formula that's why i was thinkin why are we getting ugly answer :D

35. Nnesha

$\huge\rm \frac{ f(x+h) -f(x)}{ h }$ sorry about it

36. Nnesha

|dw:1443224174112:dw|

37. Nnesha

last one is + 2a

38. Nnesha

|dw:1443224257573:dw|

39. Nnesha

$\huge\rm \frac{\frac{ -2h }{ a^2-a+ah-h-a+1 }}{ h }$ now simplify you can change division to multiplication

40. Nnesha

u there ?? o.O

41. anonymous

yes sorry i was rying to work it out

42. Nnesha

oh okay take ur time :)