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

Let's simplify the expression \( \frac{m^{x+2}-3 m^{x+1}}{3 m^{x-2}-m^{x-1}} \). First, we can factor the numerator and the denominator: **Numerator**: \[ m^{x+2} - 3 m^{x+1} = m^{x+1}(m - 3) \] **Denominator**: \[ 3 m^{x-2} - m^{x-1} = m^{x-2}(3 - m) \] Now, substituting back into our expression, we have: \[ \frac{m^{x+1}(m - 3)}{m^{x-2}(3 - m)} \] We can simplify this further. When dividing powers of the same base, we subtract the exponents: \[ = \frac{m^{x+1}}{m^{x-2}} \cdot \frac{(m - 3)}{(3 - m)} = m^{3}(m - 3)/(3 - m) \] Notice that \( 3 - m \) can be rewritten as \(-1(m - 3)\), allowing us to simplify the overall expression: \[ = -m^3 \] Thus, the simplified form of the expression is: \[ -m^3 \]