20. $$ \frac{m-2}{3 m+9} \cdot \frac{2 m+6}{2 m-4} $$

Question

UpStudy AI · Accepted Answer

To simplify the expression:

$$
\frac{m - 2}{3m + 9} \cdot \frac{2m + 6}{2m - 4}
$$

**Step 1: Factor where possible**

1. **Factor the denominators and numerators:**
   - $$3m + 9 = 3(m + 3)$$
   - $$2m + 6 = 2(m + 3)$$
   - $$2m - 4 = 2(m - 2)$$

2. **Rewrite the expression with these factors:**
   $$
   \frac{m - 2}{3(m + 3)} \cdot \frac{2(m + 3)}{2(m - 2)}
   $$

**Step 2: Cancel common factors**

1. **Cancel $$m - 2$$ in the numerator and denominator:**
   $$
   \frac{\cancel{m - 2}}{3(m + 3)} \cdot \frac{2(m + 3)}{2\cancel{(m - 2)}}
   $$

2. **Cancel $$m + 3$$ in the numerator and denominator:**
   $$
   \frac{1}{3\cancel{(m + 3)}} \cdot \frac{2\cancel{(m + 3)}}{2}
   $$

3. **Cancel the 2's:**
   $$
   \frac{1}{3} \cdot \frac{\cancel{2}}{\cancel{2}} = \frac{1}{3}
   $$

**Final Simplified Expression:**

$$
\frac{1}{3}
$$

**Note:** 
- The expression is valid as long as the original denominators are not zero. Therefore, $$m \neq -3$$ and $$m \neq 2$$.
The simplified expression is $$ \frac{1}{3} $$.

20. \( \frac{m-2}{3 m+9} \cdot \frac{2 m+6}{2 m-4} \)

Solución de tutoría real

Responder

Solución

The Deep Dive

preguntas relacionadas

Latest Algebra Questions