How to Simplify a Complex Fraction in Algebra?

[kwikness]

This is a calculus equation, but I'm having trouble with the algebra part of it.

http://calcchat.tdlc.com/solutionart/calc8e/02/e/se02e01045.gif

I'm confused about how they simplify from step 4 to 5. Can someone help me?

 

[rocomath]

$$\frac{-y+x\left(-\frac x y\right)}{y^2}\cdot\frac{\frac y 1}{\frac y 1}$$

$$\frac{-y^2-x^2}{y^3}$$

 

[sutupidmath]

$$\frac{-y+x\left(-\frac x y\right)}{y^2}\cdot\frac{\frac y 1}{\frac y 1}$$

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

you did a mistake in here! in the denominator.

 

[rocomath]

you did a mistake in here! in the denominator.

oops, I was so caught up on my latex I forgot about the denominator.

 

[kwikness]

where does the y/w come from?

 

[Gib Z]

There is no y/w.

The point is, they multiplied the numerator and denominator by y.

 

[HallsofIvy]

where does the y/w come from?

If you mean "y/1", they are just multiplying both numerator and denominator by y.

 

[Hurkyl]

kwikness: If you were asekd to simplify

[tex]\frac{1 + \frac{4}{3}}{5}[/itex]<br /> <br /> you could do it, right? What is preventing you from understanding how to simplify the fraction you asked about?[/tex]