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

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

Mathematics
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\[(1- \frac{ 5 }{ 6x })\div \frac{ 1 }{ x}-\frac{ 5 }{ 6x^2 }\]
Try a common denominator of 6x for the terms in parentheses then subtract
I think I'm supposed to flip the second one and multiply across?

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I also feel like some things would cancel?
when you divide, yes. but first you have to handle the subtraction in parentheses
Actually there are no parentheses in the question I just put them there to separate the two
ugh
or is the problem supposed to be |dw:1436129278158:dw|
right
that's the problem
that's a much easier problem :)
OK good lol
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|
crud wait. supposed to be 6x²
|dw:1436129523649:dw|
ok.. i did and its a little confusing
can you put up what you have so I can make sure we're on the same page?
sorry having trouble
yeah ill draw it
no problem. site's pretty glitchy sometimes
|dw:1436129702310:dw|
for the numerator?
|dw:1436129833564:dw|
so the numerator is\[6x^2-5x\]
why is it 6x^2 - 5x if the 6x^2 cancels to give -5? :s
the 6x² came from the 1. The -5x came from 5/(6x). You get both parts when you distribute
oh i see
why is it (-)
if we are multpying
b/c it was (-) originally and multiplied by a positive
okay
im gonna try the denominator..
ok
|dw:1436130516707:dw|
am i not cancelling when I need to
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|
You can cancel before you multiply or after. It doesn't matter. The result will be the same
do whatever you feel more comfortable with
oh okay so now I just have 6x^2 - 5x / 1/x - 5/6x^2?
and the 6x^2 cancels?
not quite: see below |dw:1436130975170:dw|
|dw:1436131068044:dw|
So you get 6x - 5 for the denominator.
and the whole thing is\[\frac{ 6x^2-5x }{ 6x-5 }\]
See where that all came from?
yes i see now. I thought you meant not to distrubute 6x^2 into any of the denominator
now to make it one term?
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
is it just x?
x(6x -5) / 6x - 5
yes. just x
oh okay. thanks so much i know that took me a while. XD
you're welcome

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