Rational Expressions and Common Denominators

This video tutorial covers adding and subtracting rational expressions with unlike monomial denominators. It emphasizes the importance of finding a common denominator and provides two examples. The first example demonstrates finding a common denominator using prime factorization for simple denominators, while the second example tackles more complex denominators. The video concludes with a summary of the key steps and checks for simplification.

What is the main requirement when adding or subtracting rational expressions?

• The expressions must be whole numbers.

• The numerators must be the same.

• The denominators must be the same.

• The expressions must be in simplest form.

How can you determine the least common denominator for 5x and 3x?

• By multiplying the numerators.

• By adding the denominators.

• By subtracting the denominators.

• By finding the least common multiple of the denominators.

What is the purpose of writing denominators in prime factored form?

• To simplify the numerators.

• To find a common denominator.

• To make the expressions more complex.

• To change the expressions to whole numbers.

In the first example, what is the common denominator for the fractions 9/15x and 10/15x?

• 5x

• 3x

• 30x

• 15x

What should you do after finding the sum of the numerators in the first example?

• Divide the sum by the denominator.

• Subtract the sum from the denominator.

• Check if the fraction can be simplified.

• Multiply the sum by the denominator.

In the second example, what is the least common denominator for the fractions with denominators 12x^2 and 9x^2?

• 9x^2

• 18x^2

• 36x^2

• 12x^2

Why is it important to ensure both denominators contain the same number of each factor?

• To ensure the expressions are whole numbers.

• To make the numerators equal.

• To simplify the expressions.

• To achieve a common denominator.

What is the result of subtracting the numerators in the second example?

• 7

• 15

• 8

• 36

What should you do if the resulting fraction after subtraction does not simplify?

• Leave it as it is.

• Subtract 1 from the denominator.

• Add 1 to the numerator.

• Multiply the fraction by 2.

What is the final step after obtaining a common denominator in any example?

• Multiply the denominators.

• Divide the numerators.

• Add or subtract the numerators.

• Multiply the numerators.