# Algebra help, Rational Equations

## Homework Statement

Solving formulas involving Rational expressions
for each excersise, solve for the indicated variable

(x-y)/xy = z

Solve for x

## The Attempt at a Solution

I started by multiplying both sides by xy, to which I got

(x-y) = xyz

Then I tried multiplying both sides by yz

(x-y)/yz = x

And from there I just get stuck, I have tried everything I can think of, and I keep losing variables... I have done a bunch of other problems of the same type... and for some reason this one (the last one) has had me stuck for the past 45 minutes.

Also, according to the back of the book, the answer is

x = y/1-yz or x = -y/yz-1

and even having the answers I can't figure out how to get there...

Thank everyone for any help, I feel like I'm going to smack myself when I finally do figure it out.

Marshall.

Related Precalculus Mathematics Homework Help News on Phys.org
Hint: put terms with "x" one the one side of equation and terms without "x" on the other

Thank you, I tried that. However, after I get:

(x-y)/yz = x

I can't seem to move the (x-y) without losing a variable somewhere, or, I could try backing up to step 2 and going to:

(x-y)/x = yz

Are either of these methods on the right track???

EDIT

Ok, I tried something else, which I feel is getting me closer,

I started here as usual:

x-y = (x)(y)(z)

Then I moved the x from the left, over to the right, and the (y)(z) from the right to the left, giving me:

-y/(y)(z) = x(-x)

But then again, this could be moving in the wrong direction...

Last edited:
symbolipoint
Homework Helper
Gold Member
Hint: put terms with "x" one the one side of equation and terms without "x" on the other
Thank you, I tried that. However, after I get:

(x-y)/yz = x

I can't seem to move the (x-y) without losing a variable somewhere, or, I could try backing up to step 2 and going to:

(x-y)/x = yz

Are either of these methods on the right track???

EDIT

Ok, I tried something else, which I feel is getting me closer,

I started here as usual:

x-y = (x)(y)(z)

Then I moved the x from the left, over to the right, and the (y)(z) from the right to the left, giving me:

-y/(y)(z) = x(-x)

But then again, this could be moving in the wrong direction...
You are on the right track but going off-track. You must concentrate on TERMS OF x, and get them all on one side, and everything else on the other side, and then you can finish in one step. Look back again on szynkasz's suggestion. That is really all you need.

Mhorton91, how did you get:

$-\frac{y}{yz}=x-x$

from:

$-y=xyz-x$

You can't divide one term on the right side by $yz$ and leave the other unchanged.

Mhorton91, how did you get:

$-\frac{y}{yz}=x-x$

from:

$-y=xyz-x$

You can't divide one term on the right side by $yz$ and leave the other unchanged.
when I had -y = (x)(y)(z)-x I divided both sides by (y)(z)

Which gave me the -y/(y)(z) = (x) -x... is that not correct?

Got it!!!

x-y/xy = z

x-y = xyz

-y = (xyz - x)

-y = x(yz-1)

-y/(yz-1) = x

Thank you for the hints!