# How do you simplify #(64x^3+1)/( 4x^2-100) * (4x+20)/(64x^2-16x+4)#?

with exclusion

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To simplify the expression (64x^3+1)/(4x^2-100) * (4x+20)/(64x^2-16x+4), we can start by factoring the numerator and denominator of each fraction separately.

The numerator of the first fraction, 64x^3+1, is a sum of cubes and can be factored as (4x+1)(16x^2-4x+1). The denominator, 4x^2-100, is a difference of squares and can be factored as (2x+10)(2x-10).

The numerator of the second fraction, 4x+20, can be factored out the common factor of 4, resulting in 4(x+5). The denominator, 64x^2-16x+4, cannot be factored further.

Now, we can cancel out any common factors between the numerators and denominators. In this case, we have a common factor of (4x+1) in the first fraction and (4x) in the second fraction.

After canceling out the common factors, the expression simplifies to:

[(4x+1)(16x^2-4x+1)] / [(2x+10)(2x-10)] * [4(x+5)] / (64x^2-16x+4)

Simplifying further is not possible without additional information or specific instructions.

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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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