Divide. Write your answer in simplest form. 3n + 1/n - 1 ÷ 2 ______

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Write Fraction Division: Write the division problem as a fraction. We have the expression (3n + 1)/(n - 1) ÷ 2. To simplify the division, we can rewrite the division by 2 as multiplication by its reciprocal, which is 1/2.Reciprocal Multiplication: Rewrite the division as multiplication by the reciprocal. The expression becomes (3n + 1)/(n - 1) * 1/2.Multiply Numerators and Denominators: Multiply the numerators and denominators. When multiplying fractions, we multiply the numerators together and the denominators together. So, we have ((3n + 1) * 1)/((n - 1) * 2).Simplify Expression: Simplify the expression. The multiplication of the numerators is straightforward since it's just (3n + 1) * 1, which is 3n + 1. The multiplication of the denominators gives us 2(n - 1), which is 2n - 2. So, the expression simplifies to (3n + 1)/(2n - 2).Factor Out Denominator: Factor out the common factor in the denominator, if possible. Looking at the denominator 2n - 2, we can factor out a 2, giving us 2(n - 1). However, since there is no common factor with the numerator 3n + 1, we cannot simplify further.

Divide. Write your answer in simplest form. $\newline$ $\frac{3n + 1}{n - 1} \div 2$

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Divide. Write your answer in simplest form. $\newline$ $\frac{3n + 1}{n - 1} \div 2$