Question
For each expression, simplify if possible. If applicable, click on "Cannot be simplified". \( \frac{6 v+5}{5 v+6}=\square \) \( \frac{v-7}{-7+v}=\square \)
Ask by Bowers Hart. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The first expression simplifies to \( \frac{6}{5} - \frac{11}{5(v+6)} \).
The second expression simplifies to 1.
Solution
Calculate or simplify the expression \( \frac{6v+5}{5v+6} \).
Divide the polynomials by following steps:
- step0: Using Long Division to Divide Polynomials:
\(\frac{6v+5}{5v+6}\)
- step1: Calculate:
\(\frac{6}{5}+\frac{-\frac{11}{5}}{5v+6}\)
Calculate or simplify the expression \( \frac{v-7}{-7+v} \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{v-7}{-7+v}\)
- step1: Reduce the fraction:
\(1\)
The simplified form of the first expression is \( \frac{6}{5} - \frac{11}{5(v+6)} \).
The simplified form of the second expression is 1.
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Simplify this solution The Deep Dive
The first expression \( \frac{6 v + 5}{5 v + 6} \) cannot be simplified further since there are no common factors to cancel out and both the numerator and denominator do not share a simple ratio. For the second expression \( \frac{v - 7}{-7 + v} \), you can rewrite the denominator as \( v - 7 \). This means it simplifies to \( \frac{v - 7}{v - 7} = 1 \) when \( v \neq 7 \). So, the simplified answer is \( 1 \) for \( v \neq 7 \).
