Solving Rational Equations: Cross Multiplying and Extraneous Solutions

This video tutorial covers solving rational equations, focusing on cross-multiplying and identifying extraneous solutions. It explains the FOIL method for solving equations and emphasizes the importance of checking solutions to avoid division by zero. The tutorial includes practice problems to reinforce understanding of these concepts.

What allows us to cross multiply when solving rational equations?

• Both sides of the equation are fractions.

• The denominators are the same.

• There are no variables in the denominators.

• The numerators are equal.

What does it mean to 'cross multiply' in the context of solving rational equations?

• Multiplying the numerators together

• Multiplying diagonally across the equals sign

• Adding the denominators together

• Subtracting the numerators from the denominators

What does FOIL stand for in the context of distributing two binomials?

• First, Outer, Inner, Last

• First, Outer, Inner, Loop

• Final, Outer, Inner, Linear

• First, Open, Inner, Last

How do you find factors of a trinomial in the form of ax^2 + bx + c?

• Numbers that multiply to a and add to c

• Numbers that multiply to c and add to b

• Numbers that multiply to b and add to c

• Numbers that multiply to b and add to a

What is the purpose of setting each factor equal to zero when solving rational equations?

• To calculate the area under the curve

• To identify the x-intercepts of the equation

• To determine the slope of the graph

• To find the maximum value of the equation

What are 'holes' in the context of rational equations?

• Maximum points on the graph

• Solutions that simplify the equation

• Values that make the denominator zero

• Points where the graph touches the x-axis

What does it mean if a solution is 'undefined' in the context of rational equations?

• The solution is valid for all real numbers

• The solution can be any number

• The solution results in division by zero

• The solution simplifies the equation

Why is it important to check your solutions in rational equations?

• To verify they do not make the denominator zero

• To confirm they are extraneous solutions

• To make sure they simplify the equation further

• To ensure they make the denominator zero

What is an extraneous solution in the context of rational equations?

• A solution that does not satisfy the original equation

• A solution that simplifies the equation

• A solution that makes the denominator zero

• A solution that is the only valid answer

How do you determine if a solution is extraneous?

• By graphing the equation

• By calculating the derivative

• By checking if it simplifies the equation

• By substituting it back into the original equation