Question
Simplify the product \( \frac{5}{n+1} \cdot \frac{n+1}{n+3} \) \( \begin{array}{l}\frac{5 n+1}{n^{2}+4 n+3} \\ \frac{5 n+5}{n^{2}+4 n+3} \\ \frac{5}{n+3} \\ \frac{5 n+1}{n+3}\end{array} \)
Ask by Osborne Mcguire. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified product is \( \frac{5}{n+3} \).
Solution
We start with the product
\[
\frac{5}{n+1} \cdot \frac{n+1}{n+3}.
\]
Since \( n+1 \) appears in both the numerator and denominator, and assuming \( n \neq -1 \), we can cancel the common factor:
\[
\frac{5}{\cancel{n+1}} \cdot \frac{\cancel{n+1}}{n+3} = \frac{5}{n+3}.
\]
Thus, the simplified expression is
\[
\frac{5}{n+3}.
\]
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Simplify this solution Extra Insights
To simplify the product \( \frac{5}{n+1} \cdot \frac{n+1}{n+3} \), we can multiply the fractions directly. When we multiply \( \frac{5}{n+1} \) by \( \frac{n+1}{n+3} \), the \( n+1 \) in the numerator of the second fraction cancels with the \( n+1 \) in the denominator of the first fraction. This leaves us with: \[ \frac{5}{n+3} \] Thus, the simplified form of the expression is \( \frac{5}{n+3} \). The correct answer is \( \frac{5}{n+3} \).
