Question
Simplify. Express your answer as a single fraction in simplest form \( \frac{8}{r+9}+5 \)
Ask by Flynn Gordon. in the United States
Jan 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\[
\frac{5r + 53}{r + 9}
\]
Solution
To simplify the expression \( \frac{8}{r+9} + 5 \) and express it as a single fraction in its simplest form, follow these steps:
1. **Find a Common Denominator:**
The denominator of the first term is \( r + 9 \). To combine the two terms, we need to express the entire expression with this common denominator.
2. **Rewrite the Whole Number as a Fraction:**
\( 5 \) can be written as \( \frac{5(r + 9)}{r + 9} \) to have the same denominator.
3. **Combine the Fractions:**
\[
\frac{8}{r+9} + \frac{5(r + 9)}{r + 9} = \frac{8 + 5(r + 9)}{r + 9}
\]
4. **Expand and Simplify the Numerator:**
\[
8 + 5(r + 9) = 8 + 5r + 45 = 5r + 53
\]
5. **Write the Final Simplified Fraction:**
\[
\frac{5r + 53}{r + 9}
\]
**Final Answer:**
\[
\frac{5r + 53}{r + 9}
\]
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Beyond the Answer
To simplify the expression \( \frac{8}{r+9} + 5 \), we need to express 5 as a fraction with the same denominator. We can write 5 as \( \frac{5(r+9)}{r+9} \). Now, we can combine the fractions: \[ \frac{8}{r+9} + \frac{5(r+9)}{r+9} = \frac{8 + 5(r+9)}{r+9} \] Now, distribute the 5 in the numerator: \[ = \frac{8 + 5r + 45}{r+9} = \frac{5r + 53}{r+9} \] Thus, the simplified expression is: \[ \frac{5r + 53}{r + 9} \]
