Simplifying Complex Algebraic Fractions

• Sep 25th 2010, 09:53 AM
BIOS
Simplifying Complex Algebraic Fractions
Need Help figuring out the following:

Simplying Complex Algebraic Fractions:

$\displaystyle \frac {y - \frac {x^2+y^2}{y}} {\frac {1}{x} - \frac {1}{y}}$

The book equates this to this:

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

It says in the book that this step reduces the numerator and denominator to single fractions. That's fine but doesn't say how it's done. I can see the top fraction you can get by:

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

But i'm still unsure of that and don't know about the bottom fraction. I would normally look to multiply like

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

then cancel out the x and y's leaving:

$y-x$

Any suggestions advice would be great.

Cheers

BIOS
• Sep 25th 2010, 10:40 AM
Zamzen
1/x - 1/y is simplified to y/xy - x/xy and u put them together into (y-x)/xy.
and the top fraction u just y^2/y to get a common denominator.
cause if u have 1/2 + 1/4 then u simplify it to 2/4 + 1/4 which u further simplify into (2 + 1) / 4
• Sep 25th 2010, 10:57 AM
Plato
Quote:

Originally Posted by BIOS
Need Help figuring out the following:

Simplying Complex Algebraic Fractions:

$\displaystyle \frac {y - \frac {x^2+y^2}{y}} {\frac {1}{x} - \frac {1}{y}}$

Multiply both numerator and denominator by $xy$.

We get $\displaystyle \frac {xy^2 - x^3-xy^2} {y-x}=\frac{-x^3}{y-x}$
• Sep 25th 2010, 11:03 AM
BIOS
Hey guys thanks for the replies.

Quote:

Originally Posted by Plato
Multiply both numerator and denominator by $xy$.

We get $\displaystyle \frac {xy^2 - x^3-xy^2} {y-x}=\frac{-x^3}{y-x}$

Hey plato. That's the answer alright. Still don't understand the books method/step in the example i posted above!

Neither do i see how you can get to xy as a common factor so easily!

Care to explain your method a little more? Would be most appreciated :)
• Sep 25th 2010, 11:22 AM
Plato
Within the complex fraction there are three 'smaller' fractions.
The common denominator of all three is $xy$
That is all there is to it.
• Sep 25th 2010, 11:30 AM
BIOS
Yeah that makes perfect sense mate thanks. Think i need to do a quick revision on fractions!

Cheers

B