icalibear one year ago Simplify to just one term (1−5/6x)÷1x−5/6x2

1. icalibear

$(1- \frac{ 5 }{ 6x })\div \frac{ 1 }{ x}-\frac{ 5 }{ 6x^2 }$

2. anonymous

Try a common denominator of 6x for the terms in parentheses then subtract

3. icalibear

I think I'm supposed to flip the second one and multiply across?

4. icalibear

I also feel like some things would cancel?

5. anonymous

when you divide, yes. but first you have to handle the subtraction in parentheses

6. icalibear

Actually there are no parentheses in the question I just put them there to separate the two

7. icalibear

ugh

8. anonymous

or is the problem supposed to be |dw:1436129278158:dw|

9. icalibear

right

10. icalibear

that's the problem

11. anonymous

that's a much easier problem :)

12. icalibear

OK good lol

13. anonymous

the denominators are 6x, x, and 6x², so their lcm (aka common denominator) is 6x². Multiplying the top and bottom by 6x² will cancel the fractions. |dw:1436129426746:dw|

14. anonymous

crud wait. supposed to be 6x²

15. anonymous

|dw:1436129523649:dw|

16. icalibear

ok.. i did and its a little confusing

17. anonymous

can you put up what you have so I can make sure we're on the same page?

18. icalibear

sorry having trouble

19. icalibear

yeah ill draw it

20. anonymous

no problem. site's pretty glitchy sometimes

21. icalibear

|dw:1436129702310:dw|

22. icalibear

for the numerator?

23. anonymous

|dw:1436129833564:dw|

24. anonymous

so the numerator is$6x^2-5x$

25. icalibear

why is it 6x^2 - 5x if the 6x^2 cancels to give -5? :s

26. anonymous

the 6x² came from the 1. The -5x came from 5/(6x). You get both parts when you distribute

27. icalibear

oh i see

28. icalibear

why is it (-)

29. icalibear

if we are multpying

30. anonymous

b/c it was (-) originally and multiplied by a positive

31. icalibear

okay

32. icalibear

im gonna try the denominator..

33. anonymous

ok

34. icalibear

|dw:1436130516707:dw|

35. icalibear

am i not cancelling when I need to

36. anonymous

It looks like you multiplied both numerator and denominator by 6x². In fraction form $$6x^2=\frac{ 6x^2 }{ 1 }$$. So only the numerator gets multiplied by it. |dw:1436130729399:dw|

37. anonymous

You can cancel before you multiply or after. It doesn't matter. The result will be the same

38. anonymous

do whatever you feel more comfortable with

39. icalibear

oh okay so now I just have 6x^2 - 5x / 1/x - 5/6x^2?

40. icalibear

and the 6x^2 cancels?

41. anonymous

not quite: see below |dw:1436130975170:dw|

42. anonymous

|dw:1436131068044:dw|

43. anonymous

So you get 6x - 5 for the denominator.

44. anonymous

and the whole thing is$\frac{ 6x^2-5x }{ 6x-5 }$

45. anonymous

See where that all came from?

46. icalibear

yes i see now. I thought you meant not to distrubute 6x^2 into any of the denominator

47. icalibear

now to make it one term?

48. anonymous

ah ok. sorry that wasn't clear. all that's left is to factor out an x on the numerator then you can cancel what's left

49. icalibear

is it just x?

50. icalibear

x(6x -5) / 6x - 5

51. anonymous

yes. just x

52. icalibear

oh okay. thanks so much i know that took me a while. XD

53. anonymous

you're welcome