Adding and Subtracting Rational Expressions 1  Summary and Q&A
TL;DR
The perimeter of a rectangle with given length and width can be expressed as 6x + 4y over x + 4, with the domain excluding x = 4.
Key Insights
 🍹 The perimeter of a rectangle is equal to the sum of its width and length multiplied by 2.
 😑 Rational expressions involve fractions where the numerator and denominator are polynomials.
 😑 Simplifying a rational expression involves finding a common denominator and adding/subtracting the numerators.
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. All right, so they give us the length the length is this rational expression, and the width is that right there. If we just draw ourselves a rectangle let's draw ourselves a rectangle up here, s... Read More
Questions & Answers
Q: How do you find the perimeter of a rectangle using rational expressions?
The perimeter is calculated by adding the width and length, each multiplied by 2. In this case, it is expressed as 2(x  3y + 2x + 5y).
Q: What is the simplified rational expression for the perimeter?
The simplified rational expression for the perimeter of the rectangle is 6x + 4y over x + 4. This expression cannot be further simplified.
Q: What is the significance of the domain in the rational expression?
The domain represents the values of x that would make the rational expression undefined. In this case, x cannot be equal to 4.
Q: How do you determine the domain for the rational expression?
To find the domain, find the values of x that would make the denominator (x + 4) equal to zero. In this case, x cannot be 4.
Summary & Key Takeaways

The perimeter of a rectangle can be found by adding the width and length multiplied by 2.

To find the perimeter as a rational expression, add the width (x  3y) and the length (2x + 5y) over a common denominator (x + 4).

Simplify the rational expression to 6x + 4y over x + 4, with x not equal to 4.