# Trouble with Rational Expression Division

• Jan 27th 2010, 11:24 PM
Noegddgeon
Trouble with Rational Expression Division
Hello, everybody. I attempted to solve a rational expression which requires division and apparently got the wrong answer. Here's the expression:

$\displaystyle \frac {\frac {x^2 - y^2}{xy}}{\frac {x - y}{y}}$

The steps I followed are as such:

1. (Turn it into multiplication):

$\displaystyle \frac {x^2 - y^2}{xy} * \frac {y}{x - y}$

$\displaystyle \frac {y(x^2 - y^2)}{xy(x - y)}$

2. Multiply:

$\displaystyle \frac {yx^2 - y^3}{yx^2 - xy^2}$

3. Simplify:

$\displaystyle \frac {y}{x}$

However, I checked the answer and apparently it's:

$\displaystyle \frac {x + y}{x}$

I'm not sure what exactly I did wrong in solving that rational expression, but any assistance in figuring it out would be greatly appreciated. :] Thank you guys for your time.

Colton
• Jan 27th 2010, 11:42 PM
fishcake
Hint:

$\displaystyle x^2-y^2 = (x+y)(x-y)$
• Jan 27th 2010, 11:44 PM
Noegddgeon
fishcake,

Thank you for your hint. That I already knew, but I took a closer look at what I was doing and thought more about it and realized I was simplifying incorrectly. I've figured out what I must do now and have learned as a result of it. Thank you anyway, I appreciate that you took the time to aid me. :]

Colton
• Jan 28th 2010, 04:42 PM
Masterthief1324
Quote:

Originally Posted by Noegddgeon
Hello, everybody. I attempted to solve a rational expression which requires division and apparently got the wrong answer. Here's the expression:

$\displaystyle \frac {\frac {x^2 - y^2}{xy}}{\frac {x - y}{y}}$

The steps I followed are as such:

1. (Turn it into multiplication):

$\displaystyle \frac {x^2 - y^2}{xy} * \frac {y}{x - y}$

$\displaystyle \frac {y(x^2 - y^2)}{xy(x - y)}$

2. Multiply:

$\displaystyle \frac {yx^2 - y^3}{yx^2 - xy^2}$

3. Simplify:

$\displaystyle \frac {y}{x}$

However, I checked the answer and apparently it's:

$\displaystyle \frac {x + y}{x}$

I'm not sure what exactly I did wrong in solving that rational expression, but any assistance in figuring it out would be greatly appreciated. :] Thank you guys for your time.

Colton

For the record: (I don't like unsolved requests)

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

1. Cancel out (x-y) because its quotient is 1. It leaves you:

$\displaystyle \frac {y(x+y)}{xy}$

2. Divide out y because its quotient is 1. It leaves you:

$\displaystyle \frac {x+y} {x}$