Rational Equation Solving Quiz

The video tutorial explains how to solve rational equations by first factoring the denominators to find the least common denominator (LCD). It then demonstrates how to clear fractions by multiplying both sides of the equation by the LCD. The tutorial continues with solving the resulting equation and emphasizes the importance of verifying solutions to identify any extraneous solutions, especially when division by zero occurs.

What is the first step in solving a rational equation?

• Multiply both sides by the numerator

• Subtract the numerators

• Factor the denominators

• Add the fractions

What is the greatest common factor of 3x - 9?

• x

• 9

• 3

• 1

What must the LCD contain for the given rational expression?

• A factor of 9

• A factor of x

• A factor of x + 3

• A factor of 3 and x - 3

What is the purpose of multiplying both sides by the LCD?

• To simplify the numerators

• To factor the numerators

• To clear the fractions from the equation

• To add fractions

What happens to the equation after multiplying by the LCD?

• It becomes a complex equation

• It remains unchanged

• It becomes a quadratic equation

• It becomes a linear equation without fractions

What is the result of distributing -18 in the equation?

• Zero

• Negative 18x

• Positive 18x

• Positive 54

What is the final step in solving the equation?

• Subtract 3 from both sides

• Add 54 to both sides

• Divide both sides by -17

• Multiply both sides by 17

Why is x=3 not a valid solution?

• It results in a negative number

• It leads to division by zero

• It is not an integer

• It is an extraneous solution

What is an extraneous solution?

• A solution that is complex

• A solution that satisfies the equation

• A solution that appears correct but is not

• A solution that is not needed

What should be done after finding a potential solution to a rational equation?

• Verify the solution

• Ignore the solution

• Multiply the solution by the LCD

• Add the solution to the equation