How do you simplify #(3x) /(x^2  2x  24) * (x  6) / (6x^2)#?
Given expression
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To simplify the expression (3x) /(x^2  2x  24) * (x  6) / (6x^2), we can follow these steps:

Factor the denominators:
 (x^2  2x  24) can be factored as (x  6)(x + 4).
 (6x^2) can be factored as 2x * 3x.

Rewrite the expression with the factored denominators:
 (3x) / [(x  6)(x + 4)] * (x  6) / (2x * 3x).

Simplify the expression by canceling out common factors:
 The (x  6) term in the numerator and denominator can be canceled out.

Simplify further:
 (3x) / [(x + 4)] * 1 / (2x * 3x).

Multiply the numerators and denominators:
 (3x) / [(x + 4)(2x * 3x)].

Combine like terms in the denominator:
 (3x) / [6x^2(x + 4)].
Therefore, the simplified expression is (3x) / [6x^2(x + 4)].
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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