Adding and Subtracting Rational Expressions With Unlike Denominators

TL;DR

Learn how to combine rational expressions with different denominators by finding common denominators and simplifying the expressions.

Transcript

in this lesson we're going to add and subtract rational expressions with unlike denominators so let's start with this example 5 over x plus 3 divided by x squared now before we can combine the two fractions we need to get common denominators so we need to multiply the first fraction on the left by x over x so that the denominators will both be x sq... Read More

Key Insights

• 😑 It is necessary to find a common denominator when adding or subtracting rational expressions with unlike denominators.
• 🧑‍🏭 After finding the common denominator, each fraction needs to be multiplied by the necessary factors to achieve the common denominator.
• 😑 Distributing and simplifying the expressions before combining them into a single fraction is crucial for obtaining the correct answer.
• 🧑‍🏭 Factoring the expressions can help identify common factors that can be canceled out.
• 😑 Simplifying the expressions helps to reduce the fractions to their simplest form.

Questions & Answers

Q: How do you add or subtract rational expressions with unlike denominators?

To add or subtract rational expressions with different denominators, you need to find a common denominator. Multiply each fraction by the necessary factors to achieve the common denominator. Then, distribute and simplify the expressions before combining them into a single fraction.

Q: What is the first step in adding or subtracting rational expressions?

The first step is to identify the common denominator. This is done by finding the least common multiple (LCM) of the denominators. Once you have the common denominator, you can proceed with multiplying each fraction by the necessary factors.

Q: Why is it important to simplify the expressions before combining them into a single fraction?

Simplifying the expressions helps to reduce the fraction to its simplest form. It also allows for easier combining of the numerators. By simplifying, you can avoid complications and errors in the final answer.

Q: Can you cancel out common factors in rational expressions when adding or subtracting?

Yes, if there are common factors in the numerator and denominator of rational expressions, they can be canceled out. This can help simplify the expressions and reduce the final answer.

Summary & Key Takeaways

• To add or subtract rational expressions, you need to find a common denominator.

• Multiply each fraction by the necessary factors to get the common denominator.

• Distribute and simplify the expressions before combining them into a single fraction.