The expression $(2 + a) : \left(\frac{1}{2} - b\right)$ involves a ratio or division. This can be rewritten as:

$\frac{2 + a}{\frac{1}{2} - b}$

Steps to simplify:

1. Rewrite the division: Dividing by a fraction is equivalent to multiplying by its reciprocal: $\frac{2 + a}{\frac{1}{2} - b} = (2 + a) \cdot \frac{1}{\frac{1}{2} - b}.$

2. Simplify the denominator: The denominator, $\frac{1}{2} - b$, cannot be simplified further unless you substitute values for $b$. If $b = \frac{1}{2}$, the denominator becomes zero, which is undefined.

Final expression:

$(2 + a) \cdot \frac{1}{\frac{1}{2} - b}$

Alternatively, you may choose to leave it as: $\frac{2 + a}{\frac{1}{2} - b}.$

If you want further operations like evaluating it for specific values of $a$ and $b$, or simplifying further, let me know!

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Questions to Explore Further:

1. Would you like to substitute specific values for $a$ and $b$?
2. Do you want to rationalize or simplify this further in a specific way?
3. Should I plot this as a function for $a$ and $b$?
4. Do you need an explanation of how dividing by a fraction works?
5. Would you like help evaluating limits as $b \to \frac{1}{2}$?

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Tip:

When dealing with expressions involving fractions in the denominator, always check if the denominator becomes zero for any value, as this will make the expression undefined.