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

- icalibear

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

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- icalibear

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

- anonymous

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

- icalibear

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

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- icalibear

I also feel like some things would cancel?

- anonymous

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

- icalibear

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

- icalibear

ugh

- anonymous

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

- icalibear

right

- icalibear

that's the problem

- anonymous

that's a much easier problem :)

- icalibear

OK good lol

- 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|

- anonymous

crud wait. supposed to be 6x²

- anonymous

|dw:1436129523649:dw|

- icalibear

ok.. i did and its a little confusing

- anonymous

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

- icalibear

sorry having trouble

- icalibear

yeah ill draw it

- anonymous

no problem. site's pretty glitchy sometimes

- icalibear

|dw:1436129702310:dw|

- icalibear

for the numerator?

- anonymous

|dw:1436129833564:dw|

- anonymous

so the numerator is\[6x^2-5x\]

- icalibear

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

- anonymous

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

- icalibear

oh i see

- icalibear

why is it (-)

- icalibear

if we are multpying

- anonymous

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

- icalibear

okay

- icalibear

im gonna try the denominator..

- anonymous

ok

- icalibear

|dw:1436130516707:dw|

- icalibear

am i not cancelling when I need to

- 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|

- anonymous

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

- anonymous

do whatever you feel more comfortable with

- icalibear

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

- icalibear

and the 6x^2 cancels?

- anonymous

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

- anonymous

|dw:1436131068044:dw|

- anonymous

So you get 6x - 5 for the denominator.

- anonymous

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

- anonymous

See where that all came from?

- icalibear

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

- icalibear

now to make it one term?

- 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

- icalibear

is it just x?

- icalibear

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

- anonymous

yes. just x

- icalibear

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

- anonymous

you're welcome

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