In the following exercises, determine the values for which the rational expression is undefined.

In the following exercises, determine the values for which...

Key Concepts

Solving for Restrictions

This process involves equating the denominator to zero and solving for the variable. It ensures that any value which causes the denominator to vanish is excluded from the domain, thereby avoiding undefined situations in the rational expression.

Zero Denominator Restriction

Since division by zero is undefined, identifying values that make the denominator zero is crucial. Setting the denominator equal to zero and solving for the variable allows one to determine the restrictions on the expression’s domain.

Domain of an Expression

The domain refers to all the possible values of the variable for which the expression is defined. For rational expressions, this typically means all real numbers except those that make the denominator zero, as division by zero is not permitted.

Rational Expressions

Rational expressions are fractions where both the numerator and the denominator are polynomials. These expressions are a fundamental component of algebra and require careful handling because their behavior is heavily influenced by the properties of polynomials in both parts of the fraction.

Transcript

00:02 Okay, number four, we want to determine the values for which each of these expressions is undefined.

00:11 They write it as a function, whatever, they could be a function too, but generally function notation would have, would be a little more formal, like i would say, f of x equals.

00:21 But in either case, you can't have zero in the denominator.

00:28 Anything over zero is undefined.

00:29 That's a big fact you've probably heard for many years now.

00:35 Division by zero doesn't exist.

00:38 So what you have to do is figure out what value or values of your variable would cause the denominator to be zero.

00:46 So essentially all you have to do is set each denominator equal to zero.

00:50 Solve it for that variable and that will tell you the value for which that function or expression is defined.

00:56 However, you've got to be careful because in part a you can actually simplify it.

00:59 A little bit, right? q squared over q, one of those cues will cancel out, which means this expression is actually 5p over 9.

01:12 Since there is no variable in the denominator, there's no way that denominator could ever equal zero, because there's no place to put in a value for a p or q.

01:22 It doesn't matter if the numerator is zero.

01:24 All that determines whether it's undefined is the denominator being zero.

01:30 So since there's no way to make that denominator zero, we simply say that this expression is defined for all real numbers...

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