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Fill in the blank to make equivalent rational expressions. \( \frac{-4}{3 w+4}=\frac{\square}{9 w+12} \)

Ask by Hart Campos. in the United States
Feb 26,2025

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The blank should be filled with –12.

Solución

To make the expressions equivalent, multiply the numerator and denominator of the left-hand side by 3:   (–4)/(3w + 4) = (–4·3)/(3w·3 + 4·3) = (–12)/(9w + 12). So, the blank should be filled with –12.

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To make these two rational expressions equivalent, you can find a common factor. The denominator \(9w + 12\) can be factored as \(3(3w + 4)\). Therefore, you can multiply the numerator of the first fraction by \(3\): \[ \frac{-4}{3w + 4} = \frac{-4 \cdot 3}{3(3w + 4)} = \frac{-12}{9w + 12}. \] So the blank should be filled with \(-12\).

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