How do you find all the values that make the expression undefined: #(3x^2 - 3)/(6x - 6)#?

Answer 1

Since division by zero results in an indetermination, your denominator cannot be zero for this expression to be undefined.

Thus, this expression becomes undefined when #6x-6=0#, thus, when #x=1#.
In this case, by the way, we'd have an interesting topic in calculus: #0/0#, but that's not the case for now.
So, your answer: this function becomes undefined only when #x=1#.
Besides, when #x=+-1#, your numerator becomes zero, but when #x=-1#, then your numerator would be #-12#, and thus, you function, #0/(-12)=0#, and zero is a defined value.
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Answer 2

To find the values that make the expression undefined, we need to identify the values that would result in a division by zero. In this case, the expression becomes undefined when the denominator (6x - 6) equals zero. Solving the equation 6x - 6 = 0, we find that x = 1. Therefore, the value x = 1 makes the expression undefined.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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