Final answer:
The expression (2)(3x+4)+(-3x-20)/(16-9x²) simplifies to (3x - 12)/(16 - 9x²), after distributing the 2 and combining like terms in the numerator.
Step-by-step explanation:
The student is asking for help with a mathematics problem involving the sum or difference of polynomial expressions and rational expressions. Specifically, the expression to simplify is (2)(3x+4)+(-3x-20)/(16-9x²). To approach this, we first distribute the 2 through the first polynomial, and then simplify the entire expression, being careful with the addition and subtraction of like terms and the distribution of negative signs.
Let's distribute and combine like terms:
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- Distribute the 2: (2)(3x) + (2)(4) = 6x + 8
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- Combine the terms: (6x + 8) + (-3x - 20)
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- Simplify: 6x + 8 - 3x - 20 = 3x - 12
The simplified expression is 3x - 12 over the given denominator, which may potentially simplify further depending on the factors of the denominator. However, since the polynomials in the numerator and the denominator do not have any common factors, this is the simplified form of the expression.