## Trying to simplify y=(2x-1)/(x-1)

Simplificatation, evaluation, linear equations, linear graphs, linear inequalities, basic word problems, etc.
landgazr
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Joined: Mon Nov 14, 2011 4:26 am
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### Trying to simplify y=(2x-1)/(x-1)

Argh...this seems so simple but I can't seem to progress beyond the first step. I am to simplify:

$y=(\frac{2x-1}{x-1})$

I am trying to isolate x.

$x=(\frac{y-1}{y-2})$

but I can't see how they got there.

For myself, I get here:

$y(x-1)=2x-1$

But every path I take from here has x propagating throughout the equation or I end up canceling x via (x-1) which is wrong of course.

Many thanks in advance for any help!

little_dragon
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Joined: Mon Dec 08, 2008 5:18 pm
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### Re: Trying to simplify y=(2x-1)/(x-1)

$y=(\frac{2x-1}{x-1})$
I am trying to isolate x.
I end up canceling x via (x-1) which is wrong of course.
how R U canceling??
do like they show here: http://www.purplemath.com/modules/solvelit.htm
go abt 2/3 down to "trick" example
then go 2 y(x-1)=2x-1
multiply out: xy-y=2x-1
get x one left
xy-2x=y-1
fac tor & divide out

landgazr
Posts: 5
Joined: Mon Nov 14, 2011 4:26 am
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### Re: Trying to simplify y=(2x-1)/(x-1)

"So keep in mind: When you can't isolate the desired variable because it is a factor in two or more terms, collect those terms together on one side of the "equals" sign, factor out the desired variable, and then divide off whatever is left."

Ah, Eureka! Thank you so much, little_dragon! That was the insight I needed!

I was trying to divide out x in the hopes that I'd be left with a single x somewhere but I see now that was totally the wrong way to go. That's what I meant by saying it was propagating because I had to divide each term by x. I guess that might have yielded a solution but I see it was really the wrong way to go anyway. This is what I should have done:

$xy-y=2x-1$
$xy-y-2x=-1$
$xy-2x=-1+y$
$xy-2x=y-1$
$x(y-2)=y-1$
$x=\frac{(y-1)}{(y-2)}$