Rational Equations and Excluded Values

This video tutorial demonstrates how to solve a rational equation by first factoring denominators to find common factors, identifying excluded values to avoid division by zero, and constructing the least common denominator. The process involves clearing fractions by multiplying both sides of the equation by the LCD and solving for the variable. The tutorial concludes with a solution check to ensure accuracy.

What is the first step in solving a rational equation as described in the video?

• Divide by the largest denominator

• Multiply each term by the numerator

• Find a common denominator

• Add all fractions together

What common factor is found in the denominator of the first fraction?

• X^2

• X

• X + 2

• X + 1

Which value must be excluded to avoid division by zero in the first fraction?

• X = 1

• X = 0

• X = -1

• X = 2

What is the least common denominator for the given fractions?

• X(X + 1)(X + 2)

• X^2 + 2X

• X + 1

• X + 2

Which of the following is not an excluded value?

• X = 0

• X = -2

• X = -1

• X = 1

What operation is performed to clear the fractions from the equation?

• Add the numerators

• Multiply by the least common denominator

• Subtract the denominators

• Divide by the least common denominator

After clearing the fractions, what is the next step in solving the equation?

• Combine like terms

• Add all terms

• Divide by the largest term

• Multiply all terms

What is the solution to the equation after simplifying?

• X = 7

• X = 1

• X = 0

• X = -7

What is the result of multiplying X by X in the equation?

• X + 1

• X

• X^2

• 2X

What is the final step in verifying the solution?

• Check if the solution is an excluded value

• Multiply the solution by the denominator

• Add the solution to the numerator

• Divide the solution by the denominator