# How do you simplify and find the restrictions for #(x^3-2x^2-8x)/(x^2-4x)#?

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The equation becomes 'undefined' if the denominator is 0. You are 'not allowed' to divide by 0.

Factorizing the top

Thus

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To simplify the expression (x^3-2x^2-8x)/(x^2-4x), we can factor out an x from the numerator and denominator, giving us x(x^2-2x-8)/(x(x-4)).

Next, we can simplify the expression in the numerator by factoring the quadratic x^2-2x-8. This factors as (x-4)(x+2).

Substituting this back into the expression, we have x(x-4)(x+2)/(x(x-4)).

Now, we can cancel out the common factors of (x-4) and x in the numerator and denominator, leaving us with (x+2)/x as the simplified expression.

To find the restrictions, we need to identify any values of x that would make the denominator equal to zero. In this case, x cannot be equal to zero or 4, as these values would result in division by zero. Therefore, the restrictions for this 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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