Rational Expressions and Equations

This video tutorial teaches how to solve fraction problems by writing and solving rational equations. It covers the basics of rational expressions, the importance of checking for extraneous solutions, and solving quadratic equations using factoring. The tutorial also explains how to handle equations involving reciprocals and complex rational expressions, ensuring no division by zero occurs. By the end, viewers will understand how to solve various rational equations and verify their solutions.

What happens to the value of a fraction if the numerator is decreased by 1 and the denominator is increased by 2?

• The value becomes one-half.

• The value remains the same.

• The value becomes three-fourths.

• The value becomes two-thirds.

What is a rational expression?

• A ratio of two integers.

• A product of two numbers.

• A sum of two fractions.

• A ratio of two polynomial expressions.

Why is it important to check for division by zero in rational equations?

• Because it ensures the equation is linear.

• Because it can lead to undefined solutions.

• Because it simplifies the equation.

• Because it makes the equation easier to solve.

What is the solution to the equation x - 1 over x + 2 equals two-thirds?

• x = 8

• x = 5

• x = 6

• x = 7

How do you verify if a solution is extraneous?

• By checking if it results in a negative number.

• By checking if it results in a positive number.

• By checking if it results in zero in the denominator.

• By checking if it results in a fraction.

What is the reciprocal of a number x?

• x squared

• 1 over x

• x plus 1

• x minus 1

What are the solutions to the equation x squared plus 6 equals 5x?

• x = 2 and x = 3

• x = 4 and x = 5

• x = 1 and x = 2

• x = 3 and x = 4

What is the sum of a number and 8 times its reciprocal if it equals 7 and one-third?

• x = 3

• x = 2

• x = 6

• x = four-thirds

What is the least common denominator used to solve the equation x plus 8 times 1 over x equals 22 thirds?

• 22

• x

• 3

• 3 and x

What are the factors of the quadratic equation 3x squared minus 22x plus 24 equals zero?

• 3x minus 4 and x minus 6

• x minus 2 and x minus 3

• x plus 2 and x plus 4

• 3x plus 4 and x plus 6