Adding and Subtracting Rational Expressions 1

TL;DR

Learn how to find the perimeter of a rectangle with given length and width, expressed as a simplified rational expression, and consider the domain restrictions.

Transcript

find the perimeter of a rectangle with the length and width given below express your answer as a simplified rational expression and state the domain so just as a little bit of a review the perimeter is just the distance around the rectangle and so if it has length w and with sorry length l and with w the perimeter is going to be this length plus w ... Read More

Key Insights

• 🍹 The perimeter of a rectangle is the sum of its length and width, each multiplied by 2.
• 😑 Rational expressions for length and width can be distributed and simplified to find the perimeter.
• 😑 The domain of the expressions is constrained by excluding the value that would make any of the denominators zero.
• 😑 The formula for the perimeter of a rectangle can be expressed as a simplified rational expression.
• 😑 The simplified rational expression for the perimeter can be factored to further simplify the expression.
• 😑 An important domain restriction for the given expressions is that x cannot be equal to -4.
• 😑 Distributing and simplifying rational expressions can help avoid finding a common denominator in adding them.

Questions & Answers

Q: What is the formula for finding the perimeter of a rectangle?

The formula for finding the perimeter of a rectangle is 2 times the sum of its length and width.

Q: How do you express the perimeter of a rectangle using rational expressions?

To express the perimeter of a rectangle using rational expressions, you distribute and simplify the rational expressions for length and width, and then apply the formula for the perimeter.

Q: What is the domain restriction for the given expressions?

The domain restriction for the given expressions is that the value of x cannot be equal to -4, as it would make the denominators of the expressions zero and result in undefined values.

Q: Can the simplified rational expression for the perimeter be further factored?

Yes, the simplified rational expression for the perimeter can be factored by pulling out a common factor like 2, resulting in a simplified expression of 2 times (3x + 2y) over (x + 4) squared, where x cannot be equal to -4.

Summary & Key Takeaways

• The perimeter of a rectangle is the sum of its length and width, each multiplied by 2.

• To find the perimeter with given expressions for length and width, distribute and simplify the rational expressions.

• The domain of the expressions is constrained by excluding the value that would make any of the denominators zero.