Simplify $$ \frac{3^{x+1}-4 \cdot 3^{x-1}}{3^{x-2}} $$

Question

UpStudy AI · Accepted Answer

To simplify the expression:

$$
\frac{3^{x+1} - 4 \cdot 3^{x-1}}{3^{x-2}}
$$

Let's break it down step by step.

1. **Express all terms with the same base and simplify the exponents:**

- $$3^{x+1} = 3 \cdot 3^x$$
   - $$4 \cdot 3^{x-1} = 4 \cdot \frac{3^x}{3} = \frac{4}{3} \cdot 3^x$$
   - $$3^{x-2} = \frac{3^x}{3^2} = \frac{3^x}{9}$$

2. **Rewrite the original expression with these substitutions:**

$$
   \frac{3 \cdot 3^x - \frac{4}{3} \cdot 3^x}{\frac{3^x}{9}}
   $$

3. **Factor out $$3^x$$ from the numerator:**

$$
   \frac{\left(3 - \frac{4}{3}\right) \cdot 3^x}{\frac{3^x}{9}} = \frac{\frac{5}{3} \cdot 3^x}{\frac{3^x}{9}}
   $$

4. **Simplify the division by multiplying by the reciprocal:**

$$
   \frac{5}{3} \cdot 3^x \times \frac{9}{3^x} = \frac{5}{3} \times 9 = 15
   $$

**Final Answer:**  
15
The simplified expression is 15.

Simplify

Upstudy AI Solution

Answer

Solution

Bonus Knowledge

Related Questions

Latest Algebra Questions