Adding and Subtracting Rational Expressions with Unlike Denominators

This lesson covers adding and subtracting rational expressions with unlike denominators. It includes multiple examples demonstrating how to find common denominators, distribute terms, and simplify expressions. The lesson also explores factoring techniques to simplify complex expressions and provides step-by-step solutions to various problems.

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

• Combine the numerators

• Factor the denominators

• Find the least common multiple of the denominators

• Multiply the expressions

How do you simplify the expression 3x - 9 - 4x - 8?

• -x - 17

• x + 1

• 7x - 17

• -7x + 1

What is the result of combining 4x + 8 and 5x - 10 with a common denominator?

• 9x - 2

• x + 2

• 9x + 18

• x - 18

After factoring, what common factors do the denominators x^2 + 9x + 20 and x^2 + 7x + 12 share?

• x + 4

• x + 5

• x + 3

• x - 4

What is the simplified form of x^2 - x - 20?

• (x - 5)(x - 4)

• (x + 5)(x + 4)

• (x + 5)(x - 4)

• (x - 5)(x + 4)

How do you handle the expression 4 - x when finding a common denominator?

• Factor out -1

• Multiply by x

• Add 4 to both sides

• Subtract x from both sides

What is the result of combining x^2 and -7 over x - 4?

• x^2 - 7x over x - 4

• x^2 - 7 over x - 4

• x^2 + 7 over x + 4

• x^2 over x - 11

What is the final form of the expression after combining 5(x^2 - 1), 2(x^2 + x - 2), and -3(x^2 + 3x + 2)?

• 4x^2 - 7x - 15

• 3x^2 + 5x + 2

• x^2 + x - 1

• 5x^2 - 2x - 3

What technique is used to simplify the expression 4x^2 - 7x - 15?

• Combining like terms

• Factoring by grouping

• Finding the least common denominator

• Distributing the negative

After factoring by grouping, what is the simplified form of 4x^2 - 7x - 15?

• (4x - 5)(x + 3)

• (x + 5)(4x - 3)

• (4x + 5)(x - 3)

• (x - 5)(4x + 3)