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Chapter 7: Problem 14

List all numbers for which each rational expression is undefined. $$ \frac{14}{-5 y} $$

Short Answer

Expert verified
The expression is undefined for \(y = 0\).

Step by step solution

01

Identify the denominator

In the rational expression \(\frac{14}{-5y}\), the denominator is \(-5y\).
02

Set the denominator equal to zero

A rational expression is undefined when its denominator is zero. Therefore, set \(-5y = 0\).
03

Solve for \(y\)

To find the value of \(y\) that makes the denominator zero, solve the equation \(-5y = 0\). Dividing both sides by \(-5\) gives \(y = 0\).
04

Identify values for which the expression is undefined

The expression \(\frac{14}{-5y}\) is undefined when \(y = 0\). Therefore, the only number for which the expression is undefined is \(y = 0\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

undefined expressions
A rational expression can become undefined. This happens when the denominator is zero. Rational expressions follow this rule because division by zero is undefined in mathematics. If you ever wonder why, think about dividing a pizza among zero friends鈥攊mpossible! Whenever you have a rational expression, checking the denominator for values that make the expression undefined is crucial. For instance, in the expression \(\frac{14}{-5y}\), to find when it is undefined, we focus on the denominator.
denominator
The denominator is the number or expression below the fraction line. It tells you into how many parts the numerator is divided. In problems with rational expressions, zero denominators make those expressions undefined. For example, in \(\frac{14}{-5y}\), \(-5y\) is the denominator.
To find out when the expression is undefined, set the denominator equal to zero: \(-5y = 0\).
Solving this for \(y\), divide both sides by \(-5\) to get \(y = 0\). Hence, the expression \(\frac{14}{-5y}\) is undefined at \(y = 0\).
solving equations
To solve equations in rational expressions, follow a step-by-step approach. This includes isolating the variable in the denominator and solving for its value. Let's practice with \(\frac{14}{-5y}\):
  • Identify the denominator: \(-5y\)
  • Set the denominator to zero: \(-5y = 0\)
  • Solve for \(y\): Divide both sides by \(-5\), giving \(y = 0\)

By solving \(-5y = 0\), you can see that \(y\) must be zero to make the denominator zero. Therefore, \(\frac{14}{-5y}\) is undefined when \(y = 0\). This systematic approach helps you determine when any rational expression is undefined.

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