# Adding and Subtracting Rational Expressions 1 | Summary and Q&A

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June 25, 2010
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Adding and Subtracting Rational Expressions 1

## 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

### 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.