MHB How to Simplify Complex Problems: Expert Tips and Tricks

[Canzy]

Hey guys,

I know it's pretty simple but after an hour of thinking on it i just can't get how to simplify this. Can someone help me?

Thank you in advance!

 

[topsquark]

Hey guys,

I know it's pretty simple but after an hour of thinking on it i just can't get how to simplify this. Can someone help me?

Thank you in advance!

Start by clearing the complex fractions. For example:
[math]\frac{\frac{1}{x} - \frac{1}{y}}{\frac{1}{x} + \frac{1}{y}}[/math]

[math]= \frac{\frac{1}{x} - \frac{1}{y}}{\frac{1}{x} + \frac{1}{y}} \cdot \frac{xy}{xy}[/math]

[math]= \frac{y - x}{y + x}[/math]

Now we pull a trick. Look at the fraction just above. I'm going to multiply the fraction by (y - x)/(y - x) to get the denominator to be of the form y^2 - x^2. That will cancel out the y^2 - x^2 in the last factor.

Can you finish this?

-Dan

 

[Canzy]

Yes, i can. Thank you!