Question
Mathias found the product \( \frac{4 x+8}{x} \cdot \frac{5}{x+2} \) as follows. \( \frac{4 x+8}{x} \cdot \frac{5}{x+2}=\frac{4 x+18}{x} \cdot \frac{5}{x+2}=\frac{12}{1} \cdot \frac{5}{x+2}=\frac{60}{x+2} \) Which of the following best describes his error? He did not multiply the denominators correctly. He did not factor the first numerator. He did not divide out the 2 from the 4 and the 8 . He did not distribute the 5 to the terms in the other numerator:
Ask by Griffin Hanson. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Mathias did not factor the first numerator correctly.
Solution
1. The correct approach is to factor the first numerator:
\[
4x+8 = 4(x+2)
\]
2. Then the product becomes:
\[
\frac{4(x+2)}{x} \cdot \frac{5}{x+2}
\]
3. Cancel the common factor \(x+2\):
\[
\frac{4}{x} \cdot 5 = \frac{20}{x}
\]
Mathias's work substituted \(4x+8\) with \(4x+18\), which indicates he failed to factor the numerator correctly.
Thus, the error is best described as: "He did not factor the first numerator."
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Extra Insights
Mathias made an error when manipulating the first numerator. The expression \(4x + 8\) can be factored as \(4(x + 2)\), but he did not do so. This oversight caused him to miss simplifying \(\frac{4(x + 2)}{x}\) alongside the \(\frac{5}{x + 2}\), which could have led to a cancellation of \(x + 2\) in the denominator. After factoring, it becomes much clearer! If he had factored \(4(x + 2)\), the expression \(\frac{4(x+2)}{x} \cdot \frac{5}{x+2}\) would simply cancel out the \(x + 2\) terms, ultimately streamlining his path to the final answer. Understanding factoring in algebra opens doors to easier calculations!
