Simplifying Rational ExpressionsDate: 06/13/2002 at 13:01:38 From: Jason Subject: what does this mean I was wondering, in this question Find (-6x^2 - 4xy + 8x)/(2x) do they want me to find out what the variables are, or do they want me to do something else with it? That is the exact way they have the question written down. Date: 06/13/2002 at 13:29:20 From: Doctor Mike Subject: Re: what does this mean Jason, They want you to simplify the expression. You can factor 2x out of the numerator, so that the numerator is 2x(-3x - 2y + 4) Then, for any non-zero x, the original expression is equal to (-3x - 2y + 4). Maybe I should add just a little to this. When you factor the numerator, then the expression becomes (2x)*(-3x-2y+4)/(2x) At this point you might want to say "Sure, just cancel the 2x terms". That is correct, but the reason you can cancel is that (2x)*(-3x-2y+4)/(2x) equals the product of fractions 2x -3x-2y+4 ---- * ---------- 2x 1 To see why this is, just think of the rule about how to multiply fractions together; namely, multiply numerators together to get the new numerator and multiply denominators together to get the new denominator. The step I did above is sort of like UN-multiplying. Anyway, once you do that, it is easy to see that (2x)/(2x) equals one whenever it makes sense at all, which is when x is not zero. See? I hope this helps. - Doctor Mike, The Math Forum http://mathforum.org/dr.math/ Date: 06/13/2002 at 13:34:34 From: Jason Subject: Thank you (what does this mean) Thank you for replying so quickly and for explaining the answer really well. I understood your response completely. Thank you again. |
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