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Chapter 6: Problem 2

Simplify each rational expression. $$\frac{34}{17}$$

Short Answer

Expert verified
The simplified form of the rational expression \(\frac{34}{17}\) is 2.

Step by step solution

01

Identifying the Rational Expression

The provided rational expression is \(\frac{34}{17}\). To simplify the expression, one should aim to express it in its most reduced form.
02

Simplifying the Rational Expression

To simplify \(\frac{34}{17}\), one needs to divide the numerator (34) by the denominator (17). This results in a quotient of 2.

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Key Concepts

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

Numerator and Denominator
In any rational expression, two primary components make up the fraction: the numerator and the denominator. The numerator is the top part of the fraction, while the denominator is the bottom. Understanding these parts can be crucial for simplifying rational expressions, as changes in these values change the fraction's value.
  • Numerator: This is the number above the fraction line. In our example, it's 34. It's the part of the fraction that indicates how many parts of the whole or group we have.
  • Denominator: This is the number below the fraction line. In this example, it's 17. It represents the total number of equal parts we are considering. It's important to remember that the denominator cannot be zero, as division by zero is undefined.
When simplifying rational expressions, the goal is to make these numbers as small as possible while keeping the fraction equivalent. This often means finding common factors between the numerator and the denominator.
Reducing Fractions
Reducing fractions involves simplifying a fraction to its smallest form. This process can involve finding the greatest common divisor (GCD) of both the numerator and the denominator and dividing them by it.Let's simplify \(\frac{34}{17}\):

  • Find the GCD of 34 and 17. In this case, 17 is a common factor of both numbers. Dividing both by 17 simplifies the fraction.
  • Perform the division: \(\frac{34 \div 17}{17 \div 17} = \frac{2}{1}\). This means the fraction simplifies to 2, as the content of the denominator, 1, doesn't affect the whole number.
Reducing makes calculations easier and results more understandable. It's a key mathematical skill that's useful in many areas.
Quotient Calculation
The quotient of a division problem is the result you get when you divide the numerator by the denominator. In the case of a rational expression like \(\frac{34}{17}\), dividing the numerator by the denominator gives a whole number result.For our example:
  • Divide 34 by 17: When you perform the division, 34 梅 17, the result is 2.
  • This means that the original fraction \(\frac{34}{17}\) can be expressed as a whole number, 2.
Understanding how to calculate the quotient from rational expressions is important for simplifying expressions and finding equivalent whole numbers. This process shows the relationship between division and fractions.

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$$\text { Solve: } x^{-2}+x^{-1}=0$$.
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