How do you simplify #(15-14x-8x^2)/ (4x^2 +4x-15) div ( 4x^2+13x-12)/(3x^2+16x+5)#?

Answer 1

This appears to be intended to be an exercise in factoring:

#15-14x-8x^2 = (5+2x)(3-4x)#
#4x^2+4x-15 = (2x-3)(2x+5)#
#4x^2+13x -12 = (4x-3)(x+4)#
#3x^2+16x+5 = (3x+1)(x+5)#

Returning to the original expression:

#(15-14x-8x^2)/(4x^2+4x-15) div (4x^2+13x -12)/(3x^2+16x+5)#
#=##color(white)("XXXX")##(15-14x-8x^2)/(4x^2+4x-15) * (3x^2+16x+5) /(4x^2+13x -12)#
#=##color(white)("XXXX")##((5+2x)(3-4x))/((2x-3)(2x+5))*((3x+1)(x+5))/((4x-3)(x+4))#
#=##color(white)("XXXX")##(cancel((5+2x))(3-4x))/((2x-3)cancel((2x+5)))*((3x+1)(x+5))/((4x-3)(x+4))#
#=##color(white)("XXXX")##(cancel((3-4x))^(-1))/((2x-3))*((3x+1)(x+5))/(cancel((4x-3))(x+4))#
#=##color(white)("XXXX")##-((3x+1)(x+5))/((2x-3)(x+4))#
or #=##color(white)("XXXX")##(3x^2+16x+5)/(2x^2+5x-12)#
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Answer 2

To simplify the expression (15-14x-8x^2)/ (4x^2 +4x-15) divided by (4x^2+13x-12)/(3x^2+16x+5), we can follow these steps:

  1. Factorize the numerators and denominators of both fractions: Numerator 1: 15-14x-8x^2 = -(8x^2 + 14x - 15) Numerator 2: 4x^2 + 13x - 12 Denominator 1: 4x^2 + 4x - 15 Denominator 2: 3x^2 + 16x + 5

  2. Rewrite the division as multiplication by flipping the second fraction: (15-14x-8x^2)/ (4x^2 +4x-15) * (3x^2 + 16x + 5)/(4x^2+13x-12)

  3. Cancel out common factors between the numerators and denominators: Numerator: -(8x^2 + 14x - 15) * (3x^2 + 16x + 5) Denominator: (4x^2 + 4x - 15) * (4x^2 + 13x - 12)

  4. Multiply the remaining factors: Numerator: -(8x^2 + 14x - 15) * (3x^2 + 16x + 5) = -24x^4 - 128x^3 - 40x^2 - 42x^3 - 224x^2 - 70x + 45x^2 + 240x + 75 Denominator: (4x^2 + 4x - 15) * (4x^2 + 13x - 12) = 16x^4 + 52x^3 - 48x^2 + 16x^3 + 52x^2 - 48x - 60x^2 - 195x + 180

  5. Combine like terms in the numerator and denominator: Numerator: -24x^4 - 170x^3 - 19x^2 + 170x + 75 Denominator: 16x^4 + 68x^3 - 108x^2 - 243x + 180

Therefore, the simplified expression is (-24x^4 - 170x^3 - 19x^2 + 170x + 75)/(16x^4 + 68x^3 - 108x^2 - 243x + 180).

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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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