Question
For each expression, simplify if possible. If applicable, dick on "Cannot be simplified" \( \frac{v+2}{-v-2}=\square \) \( \frac{8 v+3}{3 v+8}= \)
Ask by Dunn Chen. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( \frac{v+2}{-v-2} = -1 \) (when \( v \neq -2 \))
\( \frac{8v+3}{3v+8} \) cannot be simplified further.
Solution
1) For (v + 2)/(-v - 2):
Notice that -v - 2 can be factored as -(v + 2). Then:
(v + 2)/(-v - 2) = (v + 2)/[-(v + 2)] = -1, provided that v + 2 ≠ 0 (i.e. v ≠ -2).
2) For (8v + 3)/(3v + 8):
There are no common factors between the numerator and the denominator, so the expression cannot be simplified further.
Final Answers:
• (v + 2)/(-v - 2) = -1 (for v ≠ -2)
• (8v + 3)/(3v + 8) — cannot be simplified further.
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Simplify this solution Bonus Knowledge
The first expression \( \frac{v+2}{-v-2} \) can be simplified by factoring out -1 from the denominator, giving us \( -\frac{v+2}{v+2} = -1 \), provided that \( v \neq -2 \). For the second expression \( \frac{8v+3}{3v+8} \), you cannot simplify it further since the numerator and denominator do not share any common factors, so it remains as is: \( \frac{8v+3}{3v+8} \).
