How do you simplify #(x^2-x-12)/(8x^2)div(x^3+3x^2)/(8x^3-2x^2)div(4x-1)/(x+2)#?

Answer 1

#(x^2-x-12)/(8x^2)-:(x^3+3x^2)/(8x^3-2x^2)-:(4x-1)/(x+2)=((x-4)(x+2))/(4x^2)#

#(x^2-x-12)/(8x^2)-:(x^3+3x^2)/(8x^3-2x^2)-:(4x-1)/(x+2)#
= #(x^2-4x+3x-12)/(8x^2)-:(x^2(x+3))/(2x^2(4x-1))-:(4x-1)/(x+2)#
= #(x(x-4)x+3(x-4))/(8x^2)-:(x^2(x+3))/(2x^2(4x-1))-:(4x-1)/(x+2)#
= #((x+3)(x-4))/(8x^2)xx(2x^2(4x-1))/(x^2(x+3))xx(x+2)/(4x-1)#
= #(cancel((x+3))(x-4))/(4cancel(8x^2))xx(cancel((2x^2))cancel((4x-1)))/(x^2cancel((x+3)))xx(x+2)/(cancel((4x-1))#
= #((x-4)(x+2))/(4x^2)#
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Answer 2

To simplify the expression, we can follow these steps:

  1. 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)]

  2. 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)]

  3. Simplify the expression by canceling out common factors: [(x - 4)/(8x)] * [2(4x - 1)/x] * [(x + 2)/(4x - 1)]

  4. Multiply the numerators together and the denominators together: [(x - 4) * 2(4x - 1)(x + 2)] / [8x * x * (4x - 1)]

  5. Expand and simplify the numerator: [2(x - 4)(4x - 1)(x + 2)] / [8x^2(4x - 1)]

  6. Cancel out common factors: [2(x - 4)(x + 2)] / [4x^2]

  7. Simplify further if possible, but this is the final simplified expression.

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Answer from HIX Tutor

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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