Simplifying complex fraction: 1 / x - 1 / y / y / 2x - x / 2

[jlfrost]

I'm not sure how to do this but i will try to write it out because I can't figure out how to put the problem on here how it looks on my worksheet.

1 over X minus 1 over Y or (1/X-1/Y )
divided by Y over 2X minus X over 2Y or (Y/2X-X/2Y)
I believe it would look something like

1 1
__ - __
X Y
____________
Y X
__ - __
2X 2Y

If you can provide any help with that I would greatly appreciate it. It looked weird when I previewed it, but one 1 goes above the X and same for the Y and then also below the top part under the division sign Y goes over 2X and X goes over 2Y. Thank you greatly if you can understand that and provide some assistance.
Jordan

 

[arthur ohlsten]

Re: Simplifying a complex fraction

{1/x - 1/y ] / [y/2x - x/2y]

place numerator and denominator over common denominators

{[y-x]/xy} / [y^2-x^2]/2xy]

inverting and multiplying is equivalent to dividing. invert and multiply
[y-x][2xy] / [xy [y^2-x^2] ]
cancel xy and factor y^2-x^2 to [y-x][y+x]

[2[y-x] / { y-x][y+x]}
cancel y-x

2/[y+x] answer x and y not equal or equal to 0

Arthur

 

[Loren]

Re: Simplifying a complex fraction

\(\displaystyle \frac{(\frac{1}{x}-\frac{1}{y})}{(\frac{y}{2x}-\frac{x}{2y})}\cdot \frac{2xy}{2xy}\)

2xy is the lcd of all the common fractions. Take it from there.

x not equal to -y.