Rational Equations and LCD Concepts

This video tutorial covers solving rational equations by factoring denominators, determining the least common denominator (LCD), and using a graphing calculator for verification. It provides step-by-step examples, highlighting the importance of checking solutions to avoid undefined values. The tutorial emphasizes simplifying equations and verifying solutions graphically.

What is the first step in solving a rational equation according to the guidelines?

• Determine the LCD

• Check solutions

• Factor all denominators

• Multiply each side by the LCD

Why is it important to check solutions in rational equations?

• To confirm the solution is an integer

• To ensure the solution is positive

• To verify the solution does not make any denominator zero

• To check if the solution is a fraction

In Example 1, what is the LCD used to solve the equation?

• 3T

• T

• 12T

• 6T

What is the result of simplifying the equation in Example 1?

• T = 0

• T = -6

• T = 6

• T = 12

In Example 2, what is the product of the denominators used to find the LCD?

• X - 2 and X + 6

• X + 2 and X + 6

• X - 6 and X + 2

• X + 6 and X - 2

What is the solution for X in Example 2 after solving the linear equation?

• X = 1/11

• X = 2/11

• X = 3/11

• X = 4/11

In Example 3, what are the factors of the denominator that add up to positive 1?

• Positive 2 and Negative 3

• Positive 3 and Negative 2

• Positive 1 and Negative 2

• Positive 2 and Negative 1

What is the solution for X in Example 3?

• X = 2

• X = -3

• X = -2

• X = 3

In Example 4, what is the LCD determined by the factors of the denominators?

• Y + 3 and Y - 2

• Y + 2 and Y - 1

• Y + 1 and Y - 2

• Y + 2 and Y - 3

What is the final solution for Y in Example 4?

• Y = -2

• Y = 1

• Y = 2

• Y = -1