The expression in the image is:

$\frac{(2x - 4)(x + 3)}{x - 2}$

To analyze this expression, let's look at each component:

1. Numerator: $(2x - 4)(x + 3)$
2. Denominator: $x - 2$

Step-by-Step Solution

1. Identify the values that make the expression undefined:

   • The denominator $x - 2 = 0$ when $x = 2$. So, the expression is undefined at $x = 2$.

2. Simplify the expression:

   • Notice that $2x - 4$ can be factored as $2(x - 2)$.

Thus, the expression becomes:

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

3. Cancel common factors:
   • We can cancel $x - 2$ in the numerator and denominator (except where $x = 2$, as the original expression is undefined there):

$2(x + 3)$

So, the simplified expression is:

$2(x + 3)$

Note: The simplified expression is valid for all $x$ except $x = 2$.

Conclusion

The simplified form of the given algebraic expression is $2(x + 3)$, with the condition that $x \neq 2$.

Would you like more details on any specific step, or do you have any questions?

Relative Questions for Further Exploration:

1. What are the steps to simplify algebraic fractions involving polynomials?
2. How can you determine when an algebraic fraction is undefined?
3. What are the rules for factoring polynomials, and how do they apply to simplification?
4. How would this problem change if the numerator or denominator were different polynomials?
5. How can you graph the simplified expression and the original expression to compare them?

Tip:

When simplifying algebraic expressions, always check for common factors in the numerator and the denominator, but also remember to note where the expression may be undefined due to division by zero.