**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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Description: **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 tr

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Add: + 3 The LCD for the rational expressions is xy. We will multiply each one by the appropriate form of 1 to build it into an equivalent rat Since the denominators are different, we cannot add these rational expressions in their present form. Build the rational expressions so that each has a denominator of xy. y y y 3y Multiply the numerators. Multiply the denominators. 4x Add the numerators. Write the sum over the common denominator xy. ху 2. 6 Add: a b

Add: + 3 The LCD for the rational expressions is xy. We will multiply each one by the appropriate form of 1 to build it into an equivalent rat Since the denominators are different, we cannot add these rational expressions in their present form. Build the rational expressions so that each has a denominator of xy. y y y 3y Multiply the numerators. Multiply the denominators. 4x Add the numerators. Write the sum over the common denominator xy. ху 2. 6 Add: a b

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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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.

Topic Video

Question

**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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