# How do you find all the values that make the expression undefined: #(3z^2 + z)/(18z + 6)#?

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To find the values that make the expression undefined, we need to identify the values of z that would result in a denominator of zero. In this case, the expression is undefined when the denominator, 18z + 6, equals zero. Solving the equation 18z + 6 = 0, we find that z = -1/3. Therefore, the value -1/3 makes the expression undefined.

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To find all the values that make the expression undefined, you set the denominator equal to zero and solve for ( z ). In this case, the denominator is ( 18z + 6 ). Setting it equal to zero gives ( 18z + 6 = 0 ). Solving for ( z ) yields:

[ 18z + 6 = 0 ] [ 18z = -6 ] [ z = \frac{-6}{18} ] [ z = -\frac{1}{3} ]

So, the expression is undefined when ( z = -\frac{1}{3} ).

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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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