a) $$ \frac{3^{x}-3^{x}}{3^{x}+3^{x+2}} $$

Question

UpStudy AI · Accepted Answer

Let's simplify the given expression:

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

**Step 1: Simplify the Numerator**

$$
3^{x} - 3^{x} = 0
$$

**Step 2: Simplify the Denominator**

$$
3^{x} + 3^{x+2} = 3^{x} + 3^{x} \cdot 3^{2} = 3^{x} + 9 \cdot 3^{x} = (1 + 9) \cdot 3^{x} = 10 \cdot 3^{x}
$$

**Step 3: Combine Numerator and Denominator**

$$
\frac{0}{10 \cdot 3^{x}} = 0
$$

Since the denominator $$10 \cdot 3^{x}$$ is never zero for any real value of $$x$$ (because $$3^{x} > 0$$ for all real $$x$$), the entire expression simplifies to:

$$
0
$$

**Final Answer:**

0
The expression simplifies to 0.

a)

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