Find all numbers for which the rational expression is undefined.
[tex]$\frac{v+3}{v-2}$[/tex]
Answer (2)
The rational expression v − 2 v + 3 is undefined when v = 2 because the denominator becomes zero at that value. Thus, the expression cannot be evaluated for this value of v .
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A rational expression is undefined when the denominator equals zero.
Set the denominator v − 2 to zero: v − 2 = 0 .
Solve for v : v = 2 .
The expression is undefined when v = 2 .
Explanation
Understanding Undefined Rational Expressions A rational expression is undefined when its denominator is equal to zero. In this case, the rational expression is v − 2 v + 3 .
Setting the Denominator to Zero To find the values of v for which the expression is undefined, we need to find the values of v that make the denominator equal to zero. So, we set the denominator equal to zero: v − 2 = 0
Solving for v Now, we solve the equation for v :
v − 2 = 0 v = 2
Final Answer Therefore, the rational expression v − 2 v + 3 is undefined when v = 2 .
Examples
Rational expressions are used in various fields, such as physics and engineering, to model real-world phenomena. For example, in electrical engineering, rational functions can describe the impedance of a circuit as a function of frequency. Identifying when such expressions are undefined is crucial for understanding the limitations and potential issues in these models. In this case, if v represents a variable in a physical system, knowing that the expression is undefined at v=2 helps avoid situations where the model breaks down or produces nonsensical results.
