QuestionAugust 27, 2025

Select the correct answer. If no denominator equals zero, which expression is equivalent to (x+2)/(x^2)-16div (2x+4)/(x^2)+3x-4 A. (x-1)/(2(x+4)) B. (x-1)/(2(x+1)) C. (x-1)/(2(x-4)) D. ((x+2)^2)/(2(x+4)^2)

Select the correct answer. If no denominator equals zero, which expression is equivalent to (x+2)/(x^2)-16div (2x+4)/(x^2)+3x-4 A. (x-1)/(2(x+4)) B. (x-1)/(2(x+1)) C. (x-1)/(2(x-4)) D. ((x+2)^2)/(2(x+4)^2)
Select the correct answer. If no denominator equals zero, which expression is equivalent to (x+2)/(x^2)-16div (2x+4)/(x^2)+3x-4 A. (x-1)/(2(x+4)) B. (x-1)/(2(x+1)) C. (x-1)/(2(x-4)) D. ((x+2)^2)/(2(x+4)^2)

Solution
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Answer

C. \frac {x-1}{2(x-4)} Explanation 1. Simplify the division Division of fractions is equivalent to multiplying by the reciprocal. So, \frac {x+2}{x^{2}-16} \div \frac {2x+4}{x^{2}+3x-4} becomes \frac {x+2}{x^{2}-16} \times \frac {x^{2}+3x-4}{2x+4}. 2. Factor the expressions Factor x^2 - 16 as (x-4)(x+4) and 2x + 4 as 2(x+2). Factor x^2 + 3x - 4 as (x+4)(x-1). 3. Substitute factored forms Substitute the factored forms into the expression: \frac{x+2}{(x-4)(x+4)} \times \frac{(x+4)(x-1)}{2(x+2)}. 4. Cancel common factors Cancel (x+2) and (x+4) from numerator and denominator: \frac{x-1}{2(x-4)}.

Explanation

1. Simplify the division<br /> Division of fractions is equivalent to multiplying by the reciprocal. So, $\frac {x+2}{x^{2}-16} \div \frac {2x+4}{x^{2}+3x-4}$ becomes $\frac {x+2}{x^{2}-16} \times \frac {x^{2}+3x-4}{2x+4}$.<br /><br />2. Factor the expressions<br /> Factor $x^2 - 16$ as $(x-4)(x+4)$ and $2x + 4$ as $2(x+2)$. Factor $x^2 + 3x - 4$ as $(x+4)(x-1)$.<br /><br />3. Substitute factored forms<br /> Substitute the factored forms into the expression: $\frac{x+2}{(x-4)(x+4)} \times \frac{(x+4)(x-1)}{2(x+2)}$.<br /><br />4. Cancel common factors<br /> Cancel $(x+2)$ and $(x+4)$ from numerator and denominator: $\frac{x-1}{2(x-4)}$.
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