Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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Concept explainers

Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
Numbers
Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
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**Adding Rational Expressions** To add rational expressions, follow these steps: ### Example 1: **Add:** \[ \frac{3}{x} + \frac{4}{y} \] **Step 1:** Identify the Least Common Denominator (LCD). - The LCD for the rational expressions is \(xy\). We need to transform each fraction so both denominators are the same. **Step 2:** Adjust each fraction appropriately to have the same denominator \(xy\). \[ \frac{3}{x} + \frac{4}{y} = \frac{3}{x} \cdot \frac{y}{y} + \frac{4}{y} \cdot \frac{x}{x} \] **Step 3:** Write the fractions with the common denominator. \[ \frac{3y}{xy} + \frac{4x}{xy} \] **Step 4:** Add the numerators and place the result over the common denominator. \[ = \frac{3y + 4x}{xy} \] **Step 5:** Final answer. - The result is: \[ \frac{3y + 4x}{xy} \] ### Example 2: **Add:** \[ \frac{2}{a} + \frac{6}{b} \] Try out this example by following the same steps listed above. The LCD for the rational expressions will be \(ab\). Make sure to adjust each fraction to have the common denominator and then combine the numerators accordingly. By understanding how to find a common denominator and adjusting the fractions, you can easily add any set of rational expressions!
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Transcribed Image Text:**Adding Rational Expressions** To add rational expressions, follow these steps: ### Example 1: **Add:** \[ \frac{3}{x} + \frac{4}{y} \] **Step 1:** Identify the Least Common Denominator (LCD). - The LCD for the rational expressions is \(xy\). We need to transform each fraction so both denominators are the same. **Step 2:** Adjust each fraction appropriately to have the same denominator \(xy\). \[ \frac{3}{x} + \frac{4}{y} = \frac{3}{x} \cdot \frac{y}{y} + \frac{4}{y} \cdot \frac{x}{x} \] **Step 3:** Write the fractions with the common denominator. \[ \frac{3y}{xy} + \frac{4x}{xy} \] **Step 4:** Add the numerators and place the result over the common denominator. \[ = \frac{3y + 4x}{xy} \] **Step 5:** Final answer. - The result is: \[ \frac{3y + 4x}{xy} \] ### Example 2: **Add:** \[ \frac{2}{a} + \frac{6}{b} \] Try out this example by following the same steps listed above. The LCD for the rational expressions will be \(ab\). Make sure to adjust each fraction to have the common denominator and then combine the numerators accordingly. By understanding how to find a common denominator and adjusting the fractions, you can easily add any set of rational expressions!
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