How do you simplify #(15-14x-8x^2)/ (4x^2 +4x-15) div ( 4x^2+13x-12)/(3x^2+16x+5)#?
This appears to be intended to be an exercise in factoring:
Returning to the original expression:
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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:
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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
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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)
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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)
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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
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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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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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