Rational Equations and Extraneous Solutions

In this lesson, we continue exploring rational equations, focusing on finding the point of intersection between two equations. The teacher demonstrates two examples: the first involves setting equations equal and eliminating common denominators, while the second uses factoring to solve. Key concepts include simplifying equations, factoring, and identifying extraneous solutions. The lesson concludes with a summary of the methods used.

What is the main focus of today's lesson compared to yesterday's?

• Finding the value of x given y

• Finding the point of intersection of two rational equations

• Graphing linear equations

• Solving quadratic equations

In Example 1, what is the first step to find the point of intersection?

• Add the equations

• Multiply the equations

• Set the equations equal to each other

• Divide the equations

When two rational equations have the same denominator, what can you do?

• Add the denominators

• Eliminate the denominators and set the numerators equal

• Multiply the numerators

• Subtract the numerators

In Example 2, what is the first step when dealing with unlike denominators?

• Subtract the denominators

• Multiply the numerators

• Find a common denominator

• Add the numerators directly

What is the common denominator used in Example 2?

• x + 3

• x - 1

• x - 1 times x + 3

• x squared

After simplifying the equation in Example 2, what is the next step?

• Add the terms

• Move all terms to one side of the equation

• Multiply the terms

• Divide the terms

What is an extraneous solution?

• A solution that satisfies the equation

• A solution that does not satisfy the equation

• A solution that makes the denominator zero

• A solution that is negative

In Example 2, which value is identified as an extraneous solution?

• x = 2

• x = 0

• x = 6

• x = 1

What is the correct solution for Example 2 after checking for extraneous solutions?

• x = 6

• x = 0

• x = 1

• x = 2

What is the key takeaway from the lesson on solving rational equations?

• Ignore the denominators

• Always add the equations

• Multiply the equations

• Check for extraneous solutions