anonymous
  • anonymous
Are a rational expression and its simplified forms equivalent? Provide mathematical examples to support your opinions. Somebody please explain!
Mathematics
schrodinger
  • schrodinger
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schrodinger
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DeoxNA
  • DeoxNA
Just use an example you know is true: \[\frac{ 4 }{ 8 } x = \frac{ 1 }{ 2 } x \] Multiply both sides by two and you get x=x
DeoxNA
  • DeoxNA
You could forget the x part is you think of x=1, but it will work for any x.
anonymous
  • anonymous
Hmm.. okay that seems more simple than I thought, thanks!

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DeoxNA
  • DeoxNA
Anytime :)
anonymous
  • anonymous
wait wait wai.. Isn't a rational expression a ratio of two polynomials?
anonymous
  • anonymous
Wouldn't it have to be something like (x^2 +5)/(x+2)?
anonymous
  • anonymous
No... rational means it can be expressed as a fraction with integers on top and bottom
DeoxNA
  • DeoxNA
Both a ratio of polynomials and of integers are a "rational expression", and, in any case, you can use the same example to prove it for polynomials as well.
anonymous
  • anonymous
Oh, okay thanks! :)
anonymous
  • anonymous
What about ((x^2)+10)/(x+5)=x+2?
anonymous
  • anonymous
x+2 is the reduced form, but it doesn't turn out to x=x does it?

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