Simplifying Rational Expressions

The video tutorial explains how to add rational expressions by finding a common denominator, similar to adding fractions. It details the process of identifying and multiplying missing factors to achieve a common denominator, then demonstrates how to add the numerators and simplify the resulting expression. The tutorial concludes by checking if the expression can be further simplified.

Why is it necessary to have a common denominator when adding rational expressions?

• To ensure the numerators are equal

• To simplify the multiplication process

• To make the denominators identical for addition

• To avoid factoring the numerators

What is the first step in rewriting the given fractions?

• Multiplying the fractions

• Adding the numerators

• Factoring the denominators

• Putting numerators and denominators in parentheses

How do you determine the common denominator for the given fractions?

• By multiplying the existing denominators

• By adding the numerators

• By dividing the denominators

• By subtracting the numerators

What should be done to the fractions to ensure they have a common denominator?

• Subtract the denominators from the numerators

• Divide the numerators by the denominators

• Multiply both the numerator and denominator by the missing factor

• Add a constant to both numerators

What is the next step after ensuring the fractions have a common denominator?

• Multiply the denominators

• Subtract the numerators

• Combine the numerators

• Divide the numerators

How do you simplify the expression after combining the numerators?

• By multiplying the denominator

• By factoring the denominator

• By factoring the numerator

• By adding a constant

What is the common factor found in the numerator during simplification?

• 4

• 3

• 2

• 5

Why does the expression not simplify further after factoring?

• Because the expression is already in simplest form

• Because the numerator is a prime number

• Because the denominator is already simplified

• Because the factors of 27 do not add to 3

What is the final form of the rational expression after simplification?

• It remains unchanged

• It is divided by a constant

• It is multiplied by a constant

• It is added to a constant

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

• To find a common factor with the denominator

• To divide the expression by a constant

• To add a constant to the expression

• To multiply the expression by a constant