College algebra help

Find the domain of: x/x^2+x-6 Do I need to factor and solve the denominator. How would I do this?
2 minutes ago

He wants us to write in interval symbolism and Im not sure what that is. Thanks!!

Factor the denominator to find what x can't equal. I assume that all of (x^2 + x - 6) is in the denominator; x^2 + x - 6 = (x+3)(x-2), so x can't equal -3 or 2.

In interval notation, you write the endpoints of a certain range of values separated by a comma. It uses square brackets [] when the endpoints are not included (called a closed interval), and parentheses () when they are (called an open interval). If one endpoint is included, you use a parenthesis on that side and a bracket on the other. In your case, you're including everything from negative infinity up to (but not including) -3, then going from -3 to 2 (not counting either endpoint), and then from 2 to positive infinity (again, not counting 2). That's (-infinity, -3), (-3, 2), (2, infinity).

note: ( ) represent open intervals (which do NOT include the endpoints)
[ ] represent closed intervals (which DO include endpoints)

you can also have semi-closed intervals ( ] or [ )

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Is it

x/(x^2+x-6)

or

x-6+(x/x^2)

?

I'm guessing it's the first one, since there's no holes I can see in the second one. Otherwise, you have a hole wherever you'd divide by 0. So you just have to solve

x^2 + x - 6 = 0

You can solve that with the quadratic equation or factoring. Look up those terms if you don't know what they mean. However you solve it, there's two solutions. We'll call them A and B.

Interval notation means using either these brackets:

( )

or these brackets
[ ]

You can combine them. The square brackets are when you can't include the left and right edge, the parenthesis are for when you can. Your solution should look like

(-infinity, A], [A, B], [B, infinity)

I used the square brackets because you can't include A and B, since they're holes.

Yes, you have to say what numbers x can't be. Set the denominator equal to 0 and solve.

x^2 + x - 6 = 0

(x + 3)(x - 2) = 0

x can't be -3 and x can't be -2

I don't think you can really write that in interval notation. That would be something like (-inf, -3] or something similar.

I hope this information was very helpful.

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