e) $$ \frac{x^{x+2}-2^{x+3}}{2^{x+1}-2^{x+2}} $$

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UpStudy AI · Accepted Answer

Simplify the expression by following steps:
- step0: Solution:
  $$\frac{\left(x^{x+2}-2^{x+3}\right)}{\left(2^{x+1}-2^{x+2}\right)}$$
- step1: Remove the parentheses:
  $$\frac{x^{x+2}-2^{x+3}}{2^{x+1}-2^{x+2}}$$
- step2: Subtract the terms:
  $$\frac{x^{x+2}-2^{x+3}}{-2^{x+1}}$$
- step3: Rewrite the fraction:
  $$-\frac{x^{x+2}-2^{x+3}}{2^{x+1}}$$
To simplify the expression

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

we can follow these steps:

1. **Simplify the denominator**: The denominator can be factored as follows:
   $$
   2^{x+1} - 2^{x+2} = 2^{x+1}(1 - 2) = -2^{x+1}.
   $$

2. **Rewrite the expression**: Substituting the simplified denominator back into the expression gives us:
   $$
   \frac{x^{x+2} - 2^{x+3}}{-2^{x+1}}.
   $$

3. **Final expression**: This can be rewritten as:
   $$
   -\frac{x^{x+2} - 2^{x+3}}{2^{x+1}}.
   $$

Thus, the simplified form of the original expression is

$$
-\frac{x^{x+2} - 2^{x+3}}{2^{x+1}}.
$$
The simplified form of the expression is $$ -\frac{x^{x+2} - 2^{x+3}}{2^{x+1}} $$.

e)

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