Adding and Simplifying Rational Expressions

This video tutorial from Moomoomath explains how to add and subtract rational expressions, focusing on cases where the expressions do not initially have a common denominator. The instructor demonstrates factoring denominators to find common factors, writing the common denominator, and adding the expressions. The video includes examples of both factorable and non-factorable denominators, providing a step-by-step solution for each case.

What is the first step in adding rational expressions without a common denominator?

• Multiply the numerators

• Find a common denominator

• Add the denominators

• Subtract the numerators

When factoring the denominator 3x - 6, what common factor is identified?

• 2

• x

• 3

• 6

After factoring, what is the common denominator for the expressions with denominators X-2 and 3(X-2)?

• X-2

• 3

• 3(X-2)

• X-2 + 3

What operation is performed after establishing a common denominator?

• Subtract the numerators

• Add the numerators

• Multiply the denominators

• Divide the numerators

In the example using the FOIL method, what is the result of multiplying 4x by 3x?

• 7x

• 12x

• 12x^2

• 7x^2

What is the purpose of using the FOIL method in the example?

• To find the common denominator

• To simplify the expression

• To factor the expression

• To expand the expression

What is the final step after combining the expressions?

• Divide by the common denominator

• Add a constant

• Simplify the expression

• Multiply the result by 2

What is the simplified form of 12x^2 + 2x^2?

• 16x^2

• 12x^2

• 10x^2

• 14x^2

What is the result of adding -11x and 4x?

• 15x

• 7x

• -7x

• -15x

What is the constant term in the final expression?

• 1

• 2

• 3

• 0