fully reduce this fraction.

-4x+16/-6x+24

1 answer

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:

\[ \boxed{\frac{2}{3}} \]