Addition and Subtraction of Rational Algebraic Expressions I Señor Pablo TV

Summary

In this lesson for Grade 8 students, the teacher introduces the concept of adding and subtracting rational expressions, explaining the process through detailed examples. The key steps include finding the Least Common Denominator (LCD) and simplifying the terms similarly to adding and subtracting fractions. The teacher walks through the steps for several problems, demonstrating how to handle complex expressions with variables and exponents. Students are encouraged to practice more problems and are reminded that mastering this technique requires solving many examples. The video encourages interaction, inviting questions and further engagement from viewers.

Takeaways

• 😀 Addition and subtraction of rational expressions are similar to adding and subtracting fractions in elementary math.
• 😀 To solve problems, the first step is to find the Least Common Denominator (LCD) for the expressions involved.
• 😀 The LCD is determined by identifying the highest exponents of variables in the denominators.
• 😀 Once the LCD is found, divide the LCD by the denominator of each term and multiply the numerator by the remaining factor.
• 😀 After adjusting the numerators, combine them to create a single expression.
• 😀 Always simplify the resulting expression by performing arithmetic on the numerators.
• 😀 In the example 'x/y + y/x', the LCD is xy, and the result is (x² + y²) / xy.
• 😀 In the example '5/a³b + 7/ab²', the LCD is a³b², and the result is (5b + 7a²) / a³b².
• 😀 In the example '5/a²b² - 6/ab', the LCD is 6a²b², and the result is (5b - 18a) / 6a²b.
• 😀 In the example 'd/v³ - 1/v + d²/v²', the LCD is v³, and the result is (d - v² + d²v) / v³.
• 😀 It's important to remember that you cannot cancel terms across sums or differences (binomials and monomials).

Q & A

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

The first step is to find the least common denominator (LCD) of the given rational expressions, similar to adding and subtracting fractions.

How do you find the LCD of the rational expressions x/y and y/x?

The LCD is the product of the denominators, which in this case is xy. You divide the LCD by the denominator of each term and then multiply the numerator by the result.

What happens when you divide the LCD (xy) by y in the expression x/y + y/x?

When you divide xy by y, the result is x. You then multiply x by the numerator x to get x².

How do you handle the addition of the rational expressions x/y and y/x after finding the LCD?

You simplify both terms: x/y becomes x²/xy, and y/x becomes y²/xy. Then, you combine them, resulting in (x² + y²) / xy.

How do you find the LCD for the rational expressions 5/a³b and 7/ab²?

The LCD is a³b², which is the highest powers of a and b from both denominators. You divide the LCD by each denominator and multiply the result by the numerator.

What is the result of simplifying 5/a³b + 7/ab²?

After simplifying, you get (5b + 7a²) / a³b.

Can you cancel out a binomial with a monomial when simplifying rational expressions?

No, you cannot cancel a binomial with a monomial. Only factors can be canceled, and a binomial is not a factor of a monomial.

What is the LCD for the rational expressions 5/6a²b² and 3/a²b?

The LCD is 6a²b². You divide the LCD by each denominator, multiply the results by the numerators, and then combine the terms.

What happens when you subtract 6a²b²/6a²b from 5/6a²b²?

After simplifying, you get (5b - 18) / 6a²b.

What should students do to master addition and subtraction of rational expressions?

Students should practice solving many problems and feel free to ask questions if they encounter difficulties, as this topic can be tricky.