How do you simplify #(1514x8x^2)/ (4x^2 +4x15) div ( 4x^2+13x12)/(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 (1514x8x^2)/ (4x^2 +4x15) divided by (4x^2+13x12)/(3x^2+16x+5), we can follow these steps:

Factorize the numerators and denominators of both fractions: Numerator 1: 1514x8x^2 = (8x^2 + 14x  15) Numerator 2: 4x^2 + 13x  12 Denominator 1: 4x^2 + 4x  15 Denominator 2: 3x^2 + 16x + 5

Rewrite the division as multiplication by flipping the second fraction: (1514x8x^2)/ (4x^2 +4x15) * (3x^2 + 16x + 5)/(4x^2+13x12)

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)

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

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 onesided 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 onesided 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 onesided 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 onesided 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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