Pregunta
3) \( \frac{a+2 b}{6 a^{3}}-\frac{5 a+4 b}{6 a^{3}} \)
Ask by Owen Powell. in the United States
Jan 25,2025
Solución de tutoría real
Respuesta verificada por el tutor
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The simplified form of the expression is \(-\frac{2a + b}{3a^{3}}\).
Solución
To simplify the expression:
\[
\frac{a + 2b}{6a^{3}} - \frac{5a + 4b}{6a^{3}}
\]
**Step 1: Combine the Fractions**
Since both fractions have the same denominator, you can subtract the numerators directly:
\[
\frac{(a + 2b) - (5a + 4b)}{6a^{3}} = \frac{a + 2b - 5a - 4b}{6a^{3}}
\]
**Step 2: Simplify the Numerator**
Combine like terms in the numerator:
\[
a - 5a + 2b - 4b = -4a - 2b
\]
So the expression becomes:
\[
\frac{-4a - 2b}{6a^{3}}
\]
**Step 3: Factor Out Common Terms**
Factor out a \(-2\) from the numerator:
\[
\frac{-2(2a + b)}{6a^{3}}
\]
**Step 4: Reduce the Fraction**
Simplify by dividing the numerator and the denominator by 2:
\[
\frac{-2(2a + b)}{6a^{3}} = \frac{-(2a + b)}{3a^{3}}
\]
**Final Simplified Form:**
\[
-\frac{2a + b}{3a^{3}}
\]
**Answer:**
After simplifying, the expression is –(2 a + b) divided by (3 a³). In symbols,
−(2a+b)/(3a³)
Revisado y aprobado por el equipo de tutoría de UpStudy
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Bonus Knowledge
To simplify the expression, we start by combining the fractions: \[ \frac{(a + 2b) - (5a + 4b)}{6a^3} \] Now, simplify the numerator: \[ a + 2b - 5a - 4b = -4a - 2b \] Putting that back into the fraction gives us: \[ \frac{-4a - 2b}{6a^3} \] Next, we can factor out a common term from the numerator: \[ \frac{-2(2a + b)}{6a^3} \] Now, we can further simplify the fraction: \[ \frac{-2(2a + b)}{6a^3} = \frac{-(2a + b)}{3a^3} \] Thus, the simplified form of the given expression is: \[ \frac{-(2a + b)}{3a^3} \]
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