How do you simplify #(x^2-x-12)/(8x^2)div(x^3+3x^2)/(8x^3-2x^2)div(4x-1)/(x+2)#?
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To simplify the expression, we can follow these steps:
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Rewrite the expression using multiplication instead of division: [(x^2 - x - 12)/(8x^2)] * [(8x^3 - 2x^2)/(x^3 + 3x^2)] * [(x + 2)/(4x - 1)]
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Factorize the numerator and denominator of each fraction: [(x - 4)(x + 3)/(8x^2)] * [2x^2(4x - 1)/(x^2(x + 3))] * [(x + 2)/(4x - 1)]
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Simplify the expression by canceling out common factors: [(x - 4)/(8x)] * [2(4x - 1)/x] * [(x + 2)/(4x - 1)]
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Multiply the numerators together and the denominators together: [(x - 4) * 2(4x - 1)(x + 2)] / [8x * x * (4x - 1)]
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Expand and simplify the numerator: [2(x - 4)(4x - 1)(x + 2)] / [8x^2(4x - 1)]
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Cancel out common factors: [2(x - 4)(x + 2)] / [4x^2]
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Simplify further if possible, but this is the final simplified expression.
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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.
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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