Posted by Anonymous on Wednesday, September 23, 2009 at 10:38pm.
x^3x^2y over x^2y^2, divided by x^3y over xy^2+y^3
My solution: y over x
Am I right?

Algebra  Reiny, Wednesday, September 23, 2009 at 11:00pm
yes
again, what about restrictions?

Algebra  Anonymous, Wednesday, September 23, 2009 at 11:13pm
I'm fairly sure that's the extent to which I need to answer these problems.. I'm not looking for x, therefore restrictions are irrelevant

Algebra  Reiny, Wednesday, September 23, 2009 at 11:34pm
yes they are relevant
by using the = sign we are saying
"what I write next will be exactly equal to what I had before"
e.g.
(x^2  4)/(x2)
= (x+2)(x2)/(x2)
= x+2
for every value of x my last expression x+2 is equal to (x^2  4)/(x2) except when x=2
when x = 2, our first line is 0/0
but our last line is 4
so is 0/0 = 4 ????
that is why whenever we 'cancel' a variable expression we have to restrict those values that make the divided expression equal to zero.
that is ....
(x^2  4)/(x2)
= (x+2)(x2)/(x2)
= x+2 , x not equal to 2
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