Problem 2 When is a fraction or a rational... [FREE SOLUTION]

Chapter 8: Problem 2

When is a fraction or a rational expression undefined?

Short Answer

Expert verified

A fraction or rational expression is undefined when its denominator is equal to zero. For example, in the rational expression \(\frac{x}{x-2}\), it is undefined when \(x = 2\) as the denominator becomes zero. In general, to find when a rational expression is undefined, determine when its denominator is equal to zero.

Step by step solution

Identify the expression to work with

Suppose we have a generic rational expression in the form \(\frac{a}{b}\), where \(a\) and \(b\) are numbers or algebraic expressions.

Determine when the denominator is equal to zero

To find when the rational expression is undefined, we need to determine when the denominator, \(b\), is equal to zero. If \(b\) is a constant number, it is clear when it is zero or not. However, if \(b\) is an algebraic expression, we need to solve the equation \(b = 0\).

Example of a rational expression with numbers

Let's look at a simple example: \(\frac{4}{5}\). In this case, the denominator is a constant number, \(5\), which is not equal to zero, so the expression is defined.

Example of a rational expression with algebraic expressions

Now let's consider a more complex example: \(\frac{x}{x-2}\), where \(x\) is a variable. Here, the denominator is an algebraic expression, \(x-2\). We need to find when this expression is equal to zero, so we solve the equation: \(x-2 = 0\) Add \(2\) to both sides of the equation: \(x = 2\)

Conclusion

For the rational expression \(\frac{x}{x-2}\), it is undefined when \(x = 2\) because, in this case, the denominator becomes zero. In general, a fraction or rational expression is undefined when its denominator is equal to zero.

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91影视

When is a fraction or a rational expression undefined?

Short Answer

Step by step solution

Identify the expression to work with

Determine when the denominator is equal to zero

Example of a rational expression with numbers

Example of a rational expression with algebraic expressions

Conclusion

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