fractional polynomial limits

[GrahamB08]

I have a function f(x) = 2x^2 + x - 6/ x^2 +3x+2 for which I am trying to draw a graph.
in this form the value -2 is undefined.

if I factor the function I get (2x-3)(x+2)/(x+1)(x+2)
am I allowed to cancel out the (x+2)?
In the simplified form the value of -2 is defined. I am wondering if I am allowed to just used the simplified form or if I should still consider -2 as undefined.

 

[JohnZ]

I have a function f(x) = 2x^2 + x - 6/ x^2 +3x+2 for which I am trying to draw a graph.
in this form the value -2 is undefined.

if I factor the function I get (2x-3)(x+2)/(x+1)(x+2)
am I allowed to cancel out the (x+2)?
In the simplified form the value of -2 is defined. I am wondering if I am allowed to just used the simplified form or if I should still consider -2 as undefined.

you should consider -2 as undefined.
you draw graph based on (2x-3)/(x+1), but put a hole in x=-2

 

[GrahamB08]

great thanks Johnz

 

[Deleted member 4993]

I have a function f(x) = (2x^2 + x - 6)/ (x^2 +3x+2) for which I am trying to draw a graph.
in this form the value -2 is undefined.

if I factor the function I get (2x-3)(x+2)/(x+1)(x+2)
am I allowed to cancel out the (x+2)?
In the simplified form the value of -2 is defined. I am wondering if I am allowed to just used the simplified form or if I should still consider -2 as undefined.

Those () are important - super important!!!

 

[lookagain]

I have a function f(x) = (2x^2 + x - 6)/ (x^2 +3x+2) for which I am trying to draw a graph.
in this form the value -2 is undefined.

if I factor the function I get (2x-3)(x+2)/((x+1)(x+2)) \(\displaystyle \ \ \ \) <-------- And so are these.
am I allowed to cancel out the (x+2)?
In the simplified form the value of -2 is defined. I am wondering if I am allowed to just used the
simplified form or if I should still consider -2 as undefined.

Those () are important - super important!!!

.