Hart French
09/04/2024 · Middle School
1) \( \frac{a^{2}-a b+a-b}{a^{2}+2 a+1} \cdot \frac{3}{6 a^{2}-6 a b}= \)
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Step-by-step Solution
Calculate or simplify the expression \( (a^2-a*b+a-b)/(a^2+2*a+1) * (3/(6*a^2-6*a*b)) \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{\left(a^{2}-ab+a-b\right)}{\left(a^{2}+2a+1\right)}\times \left(\frac{3}{\left(6a^{2}-6ab\right)}\right)\)
- step1: Remove the parentheses:
\(\frac{a^{2}-ab+a-b}{a^{2}+2a+1}\times \left(\frac{3}{6a^{2}-6ab}\right)\)
- step2: Divide the terms:
\(\frac{a^{2}-ab+a-b}{a^{2}+2a+1}\times \frac{1}{2a^{2}-2ab}\)
- step3: Divide the terms:
\(\frac{a-b}{a+1}\times \frac{1}{2a^{2}-2ab}\)
- step4: Rewrite the expression:
\(\frac{a-b}{a+1}\times \frac{1}{2a\left(a-b\right)}\)
- step5: Reduce the fraction:
\(\frac{1}{a+1}\times \frac{1}{2a}\)
- step6: Multiply the terms:
\(\frac{1}{\left(a+1\right)\times 2a}\)
- step7: Multiply the terms:
\(\frac{1}{2a\left(a+1\right)}\)
- step8: Multiply the terms:
\(\frac{1}{2a^{2}+2a}\)
La expresión simplificada es \( \frac{1}{2a^{2}+2a} \).
Quick Answer
La expresión simplificada es \( \frac{1}{2a^{2}+2a} \).
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