Rational Expressions and Simplification

The video tutorial explains how to add and subtract rational expressions by ensuring a common denominator. It provides two examples: one for addition and one for subtraction. In each example, the process involves maintaining the common denominator, adding or subtracting the numerators, and simplifying the result by factoring and canceling common factors. The tutorial emphasizes the importance of factoring and simplification in achieving the final result.

What is necessary to add or subtract rational expressions?

• A common numerator

• Different numerators

• A common denominator

• Different denominators

When adding rational expressions with like denominators, what remains unchanged?

• The coefficients

• The numerator

• The denominator

• The entire expression

What is the first step in simplifying a rational expression after adding the numerators?

• Divide the numerators

• Factor the numerator

• Add the denominators

• Multiply the denominators

In the subtraction of rational expressions, what must be distributed to clear the parentheses?

• A zero

• A two

• A positive one

• A negative one

What is the result of combining like terms in the expression 5x^2 - 4x^2?

• 0

• 4x^2

• x^2

• 9x^2

What must be done before simplifying common factors in a rational expression?

• Add the numerator and denominator

• Factor the numerator and denominator

• Multiply the numerator and denominator

• Subtract the numerator from the denominator

Which factors are needed to factor the expression x^2 - 8x + 12?

• x - 2 and x - 6

• x - 3 and x + 6

• x + 3 and x - 6

• x + 6 and x + 2

What is the simplified form of the expression after canceling the common factor x - 6?

• x - 2

• x - 3

• x + 3

• x + 6

What is the common factor in the expression x^2 - 3x + 18?

• x + 3

• x - 6

• x + 6

• x - 3

What is the final simplified form of the expression x^2 - 8x + 12 over x^2 - 3x + 18?

• x + 2 over x - 3

• x - 2 over x + 3

• x + 2 over x + 3

• x - 2 over x - 3