Understanding Rational Equations

The video tutorial explains a method for solving rational equations by finding a common denominator. It begins with an introduction to the approach, followed by steps to find the least common denominator using prime factorization. The tutorial then demonstrates how to rewrite fractions with a common denominator, solve the equation by clearing fractions, and verify the solution for correctness.

What is the first step in solving rational equations using the new approach discussed?

• Multiply each term by a random number

• Find a common denominator for all terms

• Add all fractions together

• Subtract the smallest fraction from the largest

Why is it helpful to look at the prime factorization of denominators?

• To make the equation more complex

• To simplify the numerators

• To find the least common denominator

• To eliminate the need for a common denominator

What is the least common denominator of the fractions with denominators 5, 3, and 6?

• 10

• 60

• 15

• 30

What operation is performed after rewriting the fractions with a common denominator?

• Adding all fractions

• Dividing each term by the common denominator

• Multiplying each term by the common denominator

• Subtracting the numerators

What is the result of multiplying both sides of the equation by the least common denominator?

• The denominators become larger

• The equation becomes more complex

• The fractions are cleared from the equation

• The numerators are eliminated

What is the solution for x in the equation after clearing the fractions?

• x = 1/6

• x = 18/5

• x = 6/1

• x = 5/18

How do you verify the solution of the equation?

• By subtracting the solution from the original equation

• By adding the solution to the original equation

• By multiplying the solution by the least common denominator

• By checking if the solution satisfies the original equation

What is the common denominator used to verify the solution?

• 3

• 5

• 6

• 30

What is the simplified form of 3/5 x 5/18?

• 1/6

• 5/18

• 5/5

• 3/18

What is the next step after verifying the solution?

• Change the denominators

• Re-solve the equation

• Multiply the solution by 2

• Start a new example