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Chapter 1: Problem 771

Simplify. $$ \frac{0}{u-4.99}, \text { where } u \neq 4.99 $$

Short Answer

Expert verified
The simplified expression is 0.

Step by step solution

01

Understanding the Problem

Examine the given expression: \( \frac{0}{u-4.99} \). The problem states to simplify it given that \(u eq 4.99\).
02

Analyzing the Numerator

The numerator is 0. In any fraction, if the numerator is 0, the value of the fraction is always 0, as long as the denominator is not 0.
03

Evaluating the Denominator Condition

The condition given states \(u eq 4.99\), which ensures that the denominator \(u - 4.99\) is not zero.
04

Simplifying the Expression

Since we have established that the fraction \( \frac{0}{u-4.99} \) has a numerator of 0 and a non-zero denominator, the fraction simplifies to 0.

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Key Concepts

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

Numerator
In a fraction, the numerator is the top number. It tells us how many parts of the whole we have or how many parts we are considering. For example, in the fraction \(\frac{3}{4}\), 3 is the numerator.
In the given problem \(\frac{0}{u-4.99}\), the numerator is 0. This is important because any fraction with a numerator of 0 simplifies to 0, provided the denominator is not zero. This is true regardless of the value of the denominator, as long as it's not zero.
Whenever you encounter a fraction with a numerator of 0, you can simplify it instantly to 0. This can save you a lot of time in solving problems.
Denominator
The denominator is the bottom part of a fraction. It indicates the total number of equal parts the whole is divided into. For example, in the fraction \(\frac{3}{4}\), the denominator is 4, which means the whole is divided into 4 equal parts.
In the problem \(\frac{0}{u-4.99}\), the denominator is \(u-4.99\). The condition \(u eq 4.99\) ensures that the denominator is not zero. If the denominator were zero, the fraction would be undefined, because division by zero is not possible.
Making sure the denominator is not zero is crucial when simplifying fractions. This step avoids undefined expressions and keeps the fraction meaningful.
Simplifying Expressions
Simplifying expressions is a key skill in mathematics. It involves transforming a complex expression into a simpler form. This often makes it easier to understand and work with.
In our given problem, the expression to simplify is \(\frac{0}{u-4.99}\). Simplifying involves recognizing that any fraction with a numerator of 0 will simplify to 0, as long as the denominator is not zero. Here's the step-by-step process:
  • Identify the numerator and the denominator.
  • Check if the numerator is 0.
  • Ensure the denominator is not zero.
  • If the numerator is 0 and the denominator is non-zero, the fraction simplifies to 0.
Following these steps will help you simplify similar expressions efficiently. Practice this process to become proficient in handling fractions and rational expressions.

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