Pregunta
Simplify the rational expression. Select "Cannot be simplified" if applicable. \[ \frac{5 c-10}{2-c}=\square \]
Ask by Mann Patel. in the United States
Jan 27,2025
Solución de tutoría real
Respuesta verificada por el tutor
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\(-5\)
Solución
To simplify the rational expression:
\[
\frac{5c - 10}{2 - c}
\]
**Step 1: Factor the numerator and denominator.**
- **Numerator:** \(5c - 10 = 5(c - 2)\)
- **Denominator:** \(2 - c = -(c - 2)\)
**Step 2: Substitute the factored forms back into the expression.**
\[
\frac{5(c - 2)}{-(c - 2)}
\]
**Step 3: Simplify by canceling out the common factor \((c - 2)\).**
\[
\frac{5 \cdot \cancel{(c - 2)}}{- \cdot \cancel{(c - 2)}} = \frac{5}{-1} = -5
\]
**Note:** This simplification is valid as long as \(c \neq 2\), because if \(c = 2\), the original expression would be undefined due to division by zero.
**Final Answer:**
\(-5\)
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Mind Expander
To simplify the expression \(\frac{5c - 10}{2 - c}\), we first factor the numerator. We can factor out a 5 from the numerator to get: \[ \frac{5(c - 2)}{2 - c} \] Next, we notice that \(2 - c\) can be rewritten as \(-(c - 2)\). Thus, we have: \[ \frac{5(c - 2)}{-(c - 2)} \] Now we can cancel the \((c - 2)\) terms (as long as \(c \neq 2\)). This gives us: \[ -\frac{5}{1} = -5 \] Therefore, the simplified expression is: \[ -5 \]
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