c) $$ \frac{m^{x+2}-3 m^{x+1}}{3 m^{x-2}-m^{x-1}} $$

Question

UpStudy AI · Accepted Answer

To simplify the expression:

$$
\frac{m^{x+2} - 3m^{x+1}}{3m^{x-2} - m^{x-1}}
$$

**Step 1: Factor Common Terms**

**Numerator:**
$$
m^{x+2} - 3m^{x+1} = m^{x+1}(m - 3)
$$

**Denominator:**
$$
3m^{x-2} - m^{x-1} = m^{x-2}(3 - m)
$$

**Step 2: Rewrite the Expression**

$$
\frac{m^{x+1}(m - 3)}{m^{x-2}(3 - m)}
$$

Notice that $$ (m - 3) = -(3 - m) $$. Substituting this in:

$$
\frac{m^{x+1} \cdot -(3 - m)}{m^{x-2}(3 - m)} = -\frac{m^{x+1}}{m^{x-2}}
$$

**Step 3: Simplify the Exponents**

$$
-\frac{m^{x+1}}{m^{x-2}} = -m^{(x+1) - (x-2)} = -m^{3}
$$

**Final Answer:**

$$
-\,m^{3}
$$
$$ -\,m^{3} $$

c)