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Cancelling out x in the Nr & Dr?

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by gmatrant » Wed Aug 18, 2010 5:30 pm
Sorry a bit confused here ... can someone help me understand..

Given that (x^3+4x^2+4x)/x =9 , what is x?

x * (x^2+4x+4)/
------------------------ = x^2+4x+4 ==> Why is this wrong??
x
Why is that I cannot take x outside in the numerator as a common factory and cancel it with the x in the denominator.
There are some rules around inequalities with respect to potential negative variable.
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by selango » Wed Aug 18, 2010 6:09 pm
x * (x^2+4x+4)/
------------------------ = 9
x

You can take x as the common factor and cancel it.

x^2+4x+4 =9

x^2+4x-5=0

(x+5)(x-1) =0

x=-5 and x=1

Hope this clarify!
--Anand--
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by gmatrant » Thu Aug 19, 2010 8:16 am
If you dont cancel it you get one more root x=0. So what about that then?
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by tomada » Thu Aug 19, 2010 1:35 pm
It means that the equation is undefined at x=0, so x=0 is not a root.

gmatrant wrote:If you dont cancel it you get one more root x=0. So what about that then?
I'm really old, but I'll never be too old to become more educated.
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