Griffin Thornton
07/08/2024 · Junior High School
3. \( \frac{4 w-12 w^{2}}{2 v^{2}+8 v} \times \frac{2 v}{w} \)
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Tutor-Verified Answer
Step-by-step Solution
Calculate or simplify the expression \( (4w-12w^2)/(2v^2+8v) * 2v/w \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{\frac{\left(4w-12w^{2}\right)}{\left(2v^{2}+8v\right)}\times 2v}{w}\)
- step1: Remove the parentheses:
\(\frac{\frac{4w-12w^{2}}{2v^{2}+8v}\times 2v}{w}\)
- step2: Divide the terms:
\(\frac{\frac{2w-6w^{2}}{v^{2}+4v}\times 2v}{w}\)
- step3: Multiply the terms:
\(\frac{\frac{2\left(2w-6w^{2}\right)}{v+4}}{w}\)
- step4: Multiply by the reciprocal:
\(\frac{2\left(2w-6w^{2}\right)}{v+4}\times \frac{1}{w}\)
- step5: Rewrite the expression:
\(\frac{2w\left(2-6w\right)}{v+4}\times \frac{1}{w}\)
- step6: Reduce the fraction:
\(\frac{2\left(2-6w\right)}{v+4}\)
- step7: Simplify:
\(\frac{2^{2}-12w}{v+4}\)
- step8: Evaluate the power:
\(\frac{4-12w}{v+4}\)
The simplified form of the expression \( \frac{4w-12w^{2}}{2v^{2}+8v} \times \frac{2v}{w} \) is \( \frac{4-12w}{v+4} \).
Quick Answer
The simplified form is \( \frac{4-12w}{v+4} \).
Answered by UpStudy AI and reviewed by a Professional Tutor
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