To fully reduce the fraction \(-\frac{4x + 16}{-6x + 24}\), follow these steps:
1. **Factor the numerator and the denominator:**
First, take out the common factors in the numerator and the denominator.
- Numerator: \(-4x + 16\)
\[ -4x + 16 = -4(x - 4) \]
- Denominator: \(-6x + 24\)
\[ -6x + 24 = -6(x - 4) \]
2. **Rewrite the fraction with the factored terms:**
\[ \frac{-4(x - 4)}{-6(x - 4)} \]
3. **Cancel the common factor (x - 4):**
Since \((x - 4)\) appears in both the numerator and the denominator, they can be canceled out:
\[ \frac{-4}{-6} \]
4. **Simplify the remaining fraction:**
Divide both the numerator and denominator by their greatest common divisor, which is 2:
\[ \frac{-4 \div 2}{-6 \div 2} = \frac{-2}{-3} \]
5. **Simplify the signs:**
The negative signs in both the numerator and the denominator cancel each other out:
\[ \frac{2}{3} \]
Therefore, the fully reduced fraction is:
\[ \boxed{\frac{2}{3}} \]
fully reduce this fraction.
-4x+16/-6x+24
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