when I shouldn't cancel out denominator

[joonkimdds]

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f(x) = (x+3) / (x^2 -9)

I am tempted to simplify it into 1/ (x-3) and say this is undefined when x=3
but the solution says I shouldn't cancel top and bottom thus it's undefined
when x = +3 and x=-3.

How do I know when to simplify and when not to?

 

[dfymarine]

very simple, before you cancel each other, plug in the results to check.

 

[Streetwolf]

While (x+3) / x^2-9 and 1/(x-3) look the same mathematically, they are fact NOT the same function. Namely at the point x = -3 Note that in the second function f(-3) = -1/6 but in the first function f(-3) is UNDEFINED.

For the sake of simplifying a function you want to end at 1/(x-3).

When you need to give conditions, you MUST look at what you started with. Remember that your function is still (x+3)/x^2-9. And in that function you can't have x = -3.

So if they asked you to describe the function (x+3) / x^2-9 you would say it equals 1/(x-3) and x can't be -3 or +3.

But if they asked you to describe the function 1/(x-3) you would say that's your simplified function and x can't be +3.

 

[joonkimdds]

Is this the only type of problem that I should not simplify before answering a question?

So basically whenever I see a question like this that asks me to find when it's undefined, I should NOT simplify?

 

[Streetwolf]

The first thing you should always do is set the denominator equal to 0 and solve for x. Those are the values that you can't use. After that you can simplify.