Simphfy $$ \frac{2^{2 x}-9}{2^{x}+3} $$

Question

UpStudy AI · Accepted Answer

To simplify the expression:

$$
\frac{2^{2x} - 9}{2^x + 3}
$$

**Step 1:** Recognize that $$2^{2x}$$ can be rewritten as $$(2^x)^2$$. So, the expression becomes:

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

**Step 2:** Notice that the numerator is a difference of squares, which can be factored:

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

**Step 3:** Cancel the common term $$(2^x + 3)$$ in the numerator and the denominator:

$$
2^x - 3
$$

**Final Simplified Expression:**

$$
2^x - 3
$$
The simplified expression is $$2^x - 3$$.

Simphfy \( \frac{2^{2 x}-9}{2^{x}+3} \)