Simplify the foliowing: (a) $$ \frac{2^{2 x}-2^{x}}{2^{x}-1} $$

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To simplify the expression:

$$
\frac{2^{2x} - 2^{x}}{2^{x} - 1}
$$

Follow these steps:

1. **Rewrite the Numerator:**
   Notice that $$2^{2x}$$ can be written as $$(2^{x})^2$$. Therefore, the numerator becomes:

$$
   (2^{x})^2 - 2^{x} = 2^{x}(2^{x} - 1)
   $$

2. **Simplify the Fraction:**
   Substitute the rewritten numerator back into the original expression:

$$
   \frac{2^{x}(2^{x} - 1)}{2^{x} - 1}
   $$

The $$(2^{x} - 1)$$ terms in the numerator and denominator cancel each other out (assuming $$2^{x} - 1 \neq 0$$), leaving:

$$
   2^{x}
   $$

**Final Simplified Form:**

$$
2^{x}
$$

**Note:** The simplification holds as long as $$2^{x} - 1 \neq 0$$, which implies $$x \neq 0$$. At $$x = 0$$, the original expression is undefined (results in a $$\frac{0}{0}$$ form), whereas the simplified expression $$2^{x}$$ equals 1.

**Answer:**
After simplifying, the expression is equal to $$2^{\,x}$$.
The simplified form of the expression is $$2^{x}$$.

Simplify the foliowing:
(a)

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