the tree Posted November 2, 2006 Share Posted November 2, 2006 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? Link to comment Share on other sites More sharing options...
woelen Posted November 2, 2006 Share Posted November 2, 2006 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. Link to comment Share on other sites More sharing options...
ajb Posted November 2, 2006 Share Posted November 2, 2006 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. Link to comment Share on other sites More sharing options...
the tree Posted November 2, 2006 Author Share Posted November 2, 2006 I did, how else would I have got there? Link to comment Share on other sites More sharing options...
timo Posted November 2, 2006 Share Posted November 2, 2006 It´s not so easy to see, especially since you either made a mistake or there is a typo in above. Link to comment Share on other sites More sharing options...
the tree Posted November 2, 2006 Author Share Posted November 2, 2006 *looks over* *looks over again* *and again* hey, you're right, I did make a mistake. heh. Link to comment Share on other sites More sharing options...
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