Trouble with Rational Expression Division

**Noegddgeon** · January 27th 2010, 11:24 PM

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

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

The steps I followed are as such:

1. (Turn it into multiplication):

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

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

2. Multiply:

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

3. Simplify:

$ \frac {y}{x} $

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

$ \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

**fishcake** · January 27th 2010, 11:42 PM

Hint:

$x^2-y^2 = (x+y)(x-y)$

**Noegddgeon** · January 27th 2010, 11:44 PM

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

**Masterthief1324** · January 28th 2010, 04:42 PM

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:

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

The steps I followed are as such:

1. (Turn it into multiplication):

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

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

2. Multiply:

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

3. Simplify:

$ \frac {y}{x} $

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

$ \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)

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

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

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

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

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

Thread: Trouble with Rational Expression Division

LinkBack

Thread Tools

Display

Trouble with Rational Expression Division

Similar Math Help Forum Discussions

Rational equation, rational expression, simplifying,

[SOLVED] division of an algebric expression - no 2 (and last)

Multi Step Equations, and a little multiplication/division trouble

A complex rational equation I'm having trouble with

how to do a long division for this cube expression

Search Tags