Posted by **Anonymous** on Wednesday, September 23, 2009 at 10:38pm.

x^3-x^2y over x^2-y^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)/(x-2)

= (x+2)(x-2)/(x-2)

= x+2

for every value of x my last expression x+2 is equal to (x^2 - 4)/(x-2) **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)/(x-2)

= (x+2)(x-2)/(x-2)

= x+2 , x not equal to 2

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