Adding and Subtracting Rational Algebraic Expressions Part 2 - Grade 8 Mathematics

Summary

In this video, the teacher explains how to add and subtract rational algebraic expressions with different denominators. Using clear, step-by-step examples, viewers learn to find the least common denominator (LCD), adjust numerators, apply the distributive property, combine like terms, and simplify the final expression. The video covers three examples, including expressions with binomials and the difference of squares, highlighting techniques for factoring and canceling common terms. Perfect for students seeking a practical, easy-to-follow guide, the tutorial emphasizes understanding the process behind rational expressions, making complex algebra more approachable and reinforcing essential problem-solving skills.

Takeaways

• 😀 Adding or subtracting rational algebraic expressions is similar to working with fractions.
• 😀 When denominators are different, always find the Least Common Denominator (LCD) before combining fractions.
• 😀 Factor denominators where possible, such as using difference of squares, to simplify the process.
• 😀 To adjust each fraction, divide the LCD by the fraction’s denominator and multiply the result by the numerator.
• 😀 Combine the adjusted numerators over the common LCD.
• 😀 Simplify the numerator using the distributive property to combine like terms.
• 😀 Check for common factors between numerator and denominator and simplify further if possible.
• 😀 Example 1 shows that ⅓/(x+4) + 2/(x-2) simplifies to (5x+2)/(x^2 + 2x - 8).
• 😀 Example 2 demonstrates that factoring can reveal simplification opportunities, resulting in (3x-5)/(x^2-25) - 2/(x+5) = 1/(x-5).
• 😀 Example 3 illustrates combining fractions with binomials in denominators: (2x+1)/x + 3/(x-2) simplifies to 2(x+1)(x-1)/[x(x-2)].
• 😀 The distributive property and careful arithmetic are crucial for accurate simplification.
• 😀 Understanding and applying these steps helps manage complex rational expressions efficiently.

Q & A

What is the main topic of this video?

The main topic of the video is adding and subtracting rational algebraic expressions, specifically focusing on expressions with different denominators.

What is the first step when adding or subtracting rational expressions with different denominators?

The first step is to find the least common denominator (LCD) of the rational expressions.

How do you determine the LCD for two rational expressions?

The LCD is determined by taking the product of all distinct factors from the denominators of the expressions.

In Example 1, what are the denominators of the two rational expressions?

The denominators in Example 1 are x + 4 and x - 2.

How do you adjust each fraction once the LCD is found?

Once the LCD is found, divide the LCD by each fraction's denominator, then multiply the result by the fraction's numerator before combining the fractions.

What is the simplified result of Example 1?

The simplified result of Example 1 is (5x + 2) / ((x + 4)(x - 2)), which can also be written as (5x + 2) / (x² + 2x - 8).

How is the difference of squares used in Example 2?

In Example 2, x² - 25 is factored into (x - 5)(x + 5) using the difference of squares method.

What is the final simplified answer for Example 2?

The final simplified answer for Example 2 is 1 / (x - 5).

In Example 3, what is the LCD of the expressions 2x + 1 / x and 3 / (x - 2)?

The LCD for Example 3 is x(x - 2).

How do you simplify the numerator after multiplying by the appropriate factors in Example 3?

You apply the distributive property, combine like terms, and simplify, resulting in the numerator 2x² - x - 2, which can further factor into (2x + 1)(x - 2).

Can the denominator in Example 3 be further simplified?

Yes, the denominator x(x - 2) is already in simplified form, but if expanded, it can be written as x² - 2x.

What general rule does the video emphasize for adding and subtracting rational expressions?

The video emphasizes that adding and subtracting rational expressions is similar to adding and subtracting fractions: find the LCD, adjust each fraction accordingly, combine numerators, and simplify.