Pregunta
Subtract. \( \frac{5}{a-3}-\frac{a}{a-3} \) Simplify your answer as much as possible.
Ask by Carroll Huang. in the United States
Jan 29,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
\[
\frac{5 - a}{a - 3}
\]
Solución
To subtract the fractions \(\frac{5}{a-3}\) and \(\frac{a}{a-3}\), follow these steps:
1. **Common Denominator:**
Both fractions already have the same denominator, \(a - 3\).
2. **Subtract the Numerators:**
\[
\frac{5}{a-3} - \frac{a}{a-3} = \frac{5 - a}{a-3}
\]
3. **Simplify (Optional):**
You can also factor out a \(-1\) from the numerator if desired:
\[
\frac{5 - a}{a-3} = \frac{-(a - 5)}{a-3} = \frac{a - 5}{3 - a}
\]
However, \(\frac{5 - a}{a-3}\) is typically sufficient.
**Final Answer:**
\[
\frac{5 - a}{a - 3}
\]
Respondido por UpStudy AI y revisado por un tutor profesional
Como
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Extra Insights
To subtract the fractions \( \frac{5}{a-3} - \frac{a}{a-3} \), we can combine them since they have a common denominator: \[ \frac{5 - a}{a-3} \] Now, we can simplify the numerator. The expression \( 5 - a \) can also be written as \( -(a - 5) \), but it’s often left as is for simplicity. Thus, the simplified result is: \[ \frac{5 - a}{a-3} \] And that's the final simplified answer!
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