Rational Expressions and Simplification

The video tutorial explains how to add and subtract rational expressions by ensuring they have common denominators. It begins with factoring the denominators and then demonstrates the process of finding a common denominator for both addition and subtraction. The tutorial includes examples to illustrate the steps involved in simplifying the expressions and emphasizes the importance of factoring and combining like terms.

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

• Add the denominators

• Factor the denominators

• Subtract the numerators

• Multiply the numerators

How do you adjust a fraction if its denominator is missing a factor present in another fraction's denominator?

• Add the missing factor to the numerator

• Multiply both the numerator and denominator by the missing factor

• Subtract the missing factor from the numerator

• Divide the numerator by the missing factor

After finding a common denominator, what is the next step in adding rational expressions?

• Multiply the denominators

• Subtract the numerators

• Divide the numerators

• Add the numerators

In the first example, what is the simplified form of the expression after combining like terms?

• 4x + 3 over (x - 1)(x + 1)

• x^2 + 3x over (x - 1)(x + 1)

• x + 3 over (x - 1)(x + 1)

• 4x^2 + 3 over (x - 1)(x + 1)

What is the first step in solving a subtraction problem with different denominators?

• Factor the denominators

• Add the numerators

• Multiply the numerators

• Subtract the denominators

In the second example, what common factor is shared by both denominators initially?

• x + 5

• x + 3

• x + 2

• x + 4

How do you simplify the expression after combining like terms in the second example?

• By dividing the numerators

• By multiplying the denominators

• By factoring the numerator

• By adding more terms

What is the final simplified form of the expression in the second example?

• x - 5 over (x + 5)(x + 3)

• x + 5 over (x - 5)(x + 3)

• x - 4 over (x + 5)(x + 3)

• x + 4 over (x - 5)(x + 3)

What operation is performed after achieving a common denominator in a subtraction problem?

• Divide the numerators

• Add the numerators

• Subtract the numerators

• Multiply the numerators

What is the purpose of factoring the numerator in the final step of simplification?

• To simplify the expression

• To find a common factor

• To multiply the denominators

• To add more terms