Question
For each expression, simplify if possible. If applicable, click on "Cannot be simplified". \( \frac{2 v+3}{3 v+2}=\square \) \( \frac{-v-5}{v+5}=\square \)
Ask by Ortiz Bob. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Simplify the expressions:
1. \( \frac{2v+3}{3v+2} = \frac{2}{3} + \frac{\frac{5}{3}}{3v+2} \)
2. \( \frac{-v-5}{v+5} = -1 \)
Solution
Calculate or simplify the expression \( \frac{2v+3}{3v+2} \).
Divide the polynomials by following steps:
- step0: Using Long Division to Divide Polynomials:
\(\frac{2v+3}{3v+2}\)
- step1: Calculate:
\(\frac{2}{3}+\frac{\frac{5}{3}}{3v+2}\)
Calculate or simplify the expression \( \frac{-v-5}{v+5} \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{-v-5}{v+5}\)
- step1: Rewrite the fraction:
\(-\frac{v+5}{v+5}\)
- step2: Reduce the fraction:
\(-1\)
The simplified form of the first expression is \( \frac{2}{3} + \frac{\frac{5}{3}}{3v+2} \) and the simplified form of the second expression is -1.
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Simplify this solution Mind Expander
To tackle the first expression \( \frac{2 v+3}{3 v+2} \), you can see that it can’t be simplified further since the numerator and denominator share no common factors. So, the answer is: Cannot be simplified. For the second expression \( \frac{-v-5}{v+5} \), notice that you can factor out a negative sign from the numerator. This gives you \( \frac{-(v+5)}{v+5} \). The \( v+5 \) terms cancel out (as long as \( v \neq -5 \)), leaving you with -1. So, the answer is: -1.
