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 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.
The simplified form of the expression is $$-m^{3}$$.

c)

Upstudy AI Solution

Answer

Solution

Extra Insights

Related Questions

Latest Algebra Questions