Question
Add. \( \frac{4}{c+3}+\frac{7}{c+3} \) simplify your answer as much as possible.
Ask by Watson Ryan. in the United States
Jan 29,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\[
\frac{11}{c + 3}
\]
Solution
To add the fractions \(\frac{4}{c+3}\) and \(\frac{7}{c+3}\), follow these steps:
1. **Ensure the denominators are the same:**
Both fractions have the same denominator, \(c + 3\).
2. **Add the numerators:**
\[
\frac{4}{c+3} + \frac{7}{c+3} = \frac{4 + 7}{c + 3}
\]
3. **Simplify the numerator:**
\[
\frac{4 + 7}{c + 3} = \frac{11}{c + 3}
\]
**Final Simplified Form:**
\[
\frac{11}{c + 3}
\]
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Simplify this solution Extra Insights
When you add the fractions \( \frac{4}{c+3} + \frac{7}{c+3} \), you can combine them since they have the same denominator. This gives you \( \frac{4 + 7}{c + 3} = \frac{11}{c + 3} \). So, the simplified form of the expression is \( \frac{11}{c + 3} \). Now, remember that this expression is valid as long as \( c \neq -3 \) because that would make the denominator zero, which is undefined in mathematics!
