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

To simplify the expression: \[ \frac{m^{x+2} - 3m^{x+1}}{3m^{x-2} - m^{x-1}} \] **Step 1: Factor the Numerator and Denominator** - **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 with Factored Terms** \[ \frac{m^{x+1}(m - 3)}{m^{x-2}(3 - m)} \] **Step 3: Simplify the Fraction** Notice that \(3 - m = -(m - 3)\). Substitute this into the denominator: \[ \frac{m^{x+1}(m - 3)}{m^{x-2}(-1)(m - 3)} = \frac{m^{x+1}}{m^{x-2}} \cdot \frac{m - 3}{-(m - 3)} \] Cancel out the \((m - 3)\) terms: \[ \frac{m^{x+1}}{m^{x-2}} \cdot (-1) = -\frac{m^{x+1}}{m^{x-2}} \] **Step 4: Simplify the Exponents** Subtract the exponents in the fraction: \[ -\frac{m^{x+1}}{m^{x-2}} = -m^{(x+1) - (x-2)} = -m^{3} \] **Final Simplified Form:** \[ - m^{3} \] **Answer:** After simplifying, the expression equals –m cubed. In symbols, its simplified form is – m³.