# How do you find all numbers that must be excluded from the domain of the given rational expression #8/(x^2-4x)#?

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To find the numbers that must be excluded from the domain of the given rational expression 8/(x^2-4x), we need to identify the values of x that would result in division by zero. In this case, division by zero occurs when the denominator (x^2-4x) equals zero.

To solve for x, we set the denominator equal to zero and solve the equation:

x^2 - 4x = 0

Factoring out x, we get:

x(x - 4) = 0

Setting each factor equal to zero, we have:

x = 0 or x - 4 = 0

Solving for x in each equation, we find:

x = 0 or x = 4

Therefore, the numbers that must be excluded from the domain of the given rational expression are x = 0 and x = 4.

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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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