Final answer:
To find the excluded values of x in a rational expression, set the denominator equal to zero and solve for x. Simplify algebra and check answers to ensure reasonability. In quadratic equations, discard solutions that are not physically possible.
Step-by-step explanation:
The student's question relates to finding excluded values of x in a rational expression. Excluded values are values for x that would make the denominator of the expression equal to zero, as division by zero is undefined. To determine these excluded values, we look at the denominators within the expression and set them equal to zero and solve for x. For instance, if the denominator included factors like (x+7) and (x-7), the excluded values would be x ≠ -7 and x ≠ 7 respectively.
When simplifying algebraic expressions, it's important to eliminate terms wherever possible to make the expression more manageable. Once simplified, we check the answer to ensure that it makes sense in the context of the problem. If a certain value of x results in a physically impossible situation (such as a negative concentration), that value can be disregarded.
If dealing with quadratic equations, we can use the quadratic formula to find potential values for x. However, sometimes one of the solutions will not be reasonable in a real-world context and can thus be excluded. For example, a negative result in situations where only positive values are reasonable (like concentrations or distances) would be discarded.