Quiz on Solving Rational Equations and Inequalities

What is the first step in solving a rational equation?

• Divide by the largest coefficient

• Factor all numerators

• Add all terms to one side

• Multiply each term by the least common denominator

Why is it important to ensure the denominator does not equal zero?

• To avoid undefined expressions

• To make the equation linear

• To ensure all terms are positive

• To simplify the equation

In the first example, what is the least common multiple between 24 and 4?

• 4

• 48

• 12

• 24

What should you do after multiplying by the least common denominator?

• Add all terms to one side

• Divide by the largest coefficient

• Simplify and solve the equation

• Factor the numerators

What is the purpose of factoring the denominators in the second example?

• To make the equation linear

• To find the least common denominator

• To simplify the numerators

• To eliminate extraneous solutions

What is an extraneous solution?

• A solution that makes the numerator zero

• A solution that makes the denominator zero

• A solution that is greater than one

• A solution that is less than zero

What is the first step in solving a rational inequality?

• Solve the related equation

• State the excluded values

• Test intervals on a number line

• Multiply by the least common denominator

How do you determine the intervals to test in a rational inequality?

• By simplifying the inequality

• By factoring the numerators

• By dividing the number line at excluded values

• By solving the related equation

In the final example, what is the common denominator used?

• 9K

• 9

• 3

• K

What should you do after finding the excluded values in a rational inequality?

• Multiply by the least common denominator

• Test values in each interval

• Add all terms to one side

• Solve the related equation