# [SOLVED] Complex rational expressions HELP!

• Nov 6th 2007, 11:05 AM
JessicaHoaglund
[SOLVED] Complex rational expressions HELP!
I do not understand how to do these problems. Is there anyone who understands these?

3x/y - x
______________
2y - y/x
• Nov 6th 2007, 11:06 AM
Jhevon
Quote:

Originally Posted by JessicaHoaglund
I do not understand how to do these problems. Is there anyone who understands these?

3x/y - x
______________
2y - y/x

please verify, is this supposed to be $\frac {\frac {3x}y - x}{2y - \frac yx}$ ?

and what do you want to do? simplify?
• Nov 6th 2007, 11:08 AM
JessicaHoaglund
Yes. I am new to this site and am not exactly sure how to type it that way, but yes I need to simplify. THANKS!
• Nov 6th 2007, 11:18 AM
Krizalid
What about if you multiply the complex fraction (top & bottom) by $xy\,?$
• Nov 6th 2007, 11:18 AM
Jhevon
Quote:

Originally Posted by JessicaHoaglund
Yes. I am new to this site and am not exactly sure how to type it that way, but yes I need to simplify. THANKS!

the easiest way i'm seeing is to just combine the fractions in the numerator and the denominator and then simplify:

$\frac {\frac {3x}y - x}{2y - \frac yx} = \frac {\frac {3x - xy}y}{\frac {2xy - y}x} = \frac {x(3 - y)}y \cdot \frac x{y(2x - 1)} = \frac {x^2 (3 - y)}{y^2 (2x - 1)}$

...or yes, you can do it Krizalid's way. i thought about it, but for some reason i decided to do it the hard way.