Is there a formal definition to "simplifying"?

[the tree]

I've been doing exercises that require simplifying expressions since forever, but I don't think I ever questioned what it actually meant.

The reason I ask was that I came across this expression: [math](\frac{x+y}{y+z})^{2}(y^{2}-z^{2})[/math]

And tried to simplify it, I got to [math](x^{2} + y^{2} + \frac{2xy}{y+z})(y-z)[/math]

and then thought, hey, is that actually any simpler?

[woelen]

As far as I know there is no real definition of what is simple.

 

Simplyfying usually means making the expression shorter. In this case, I hardly would call it simpler.

 

Usually, manipulating mathematical expressions is done with a certain goal. The concept of simple then is something, which depends on the goal.

 

Which of the two following expressions would you call simpler?

 

ax² + bx + c

 

a(x + b/2a)² + c - b²/4a

 

Probably the first, but their values are the same.

 

But if it comes to solving the equation ax² + bx + c = 0, then the latter is more convenient.

 

Solving the quadratic equation now simply is taking the constant term to the right, dividing it by a, and taking the square root of it. So, simplifying usually is with a goal, and the goal determines what you think is simplest.

[ajb]

I agree with woelen, I don't think there is a definition of "simplify".

 

However for your expression you could use the difference of two squares to cancel a y+z in the denominator.

[the tree]

I did, how else would I have got there?

[timo]

It´s not so easy to see, especially since you either made a mistake or there is a typo in above.

[the tree]

*looks over*

*looks over again*

*and again*

 

hey, you're right, I did make a mistake. heh.