Solving Rational Equations and Binomials

This video tutorial covers solving rational equations using cross multiplication. It begins with an introduction to the concept, followed by detailed steps to solve quadratic equations through factoring. The tutorial emphasizes the importance of checking solutions for accuracy. Several example problems are solved to demonstrate the techniques, and advanced methods like FOIL are introduced for more complex equations.

What is the primary focus of this lesson on solving rational equations?

• Graphing equations

• Simplifying expressions

• Cross-multiplying

• Adding and subtracting fractions

When cross-multiplying with a binomial, what must you remember to do?

• Put parentheses around the binomial

• Subtract the terms

• Divide the terms

• Add the terms

What is the first step in solving a quadratic equation after cross-multiplying?

• Divide both sides by 12

• Multiply both sides by 12

• Subtract 12 from both sides

• Add 12 to both sides

What should you do after factoring a quadratic equation?

• Set the factors equal to zero

• Add the factors

• Divide the factors

• Multiply the factors

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

• To ensure the solutions are positive

• To simplify the equation further

• To verify the solutions are correct

• To find more solutions

In the second example, what are the factors of negative 15 that add to negative 2?

• -5 and -3

• -3 and 5

• -5 and 3

• 5 and 3

What method is used to solve equations involving binomials?

• Substitution

• Graphing

• FOIL method

• Cross-multiplying

What is the result of combining like terms in the FOIL method example?

• 5H and 3H

• Negative 6H and 1H

• 6H and 1H

• Negative 5H and 2H

What is the final step in solving for H in the FOIL method example?

• Divide by 15

• Add 15 to both sides

• Subtract 15 from both sides

• Multiply by 15

What should you do if you get a fraction as a solution?

• Ignore it

• Check it

• Simplify it

• Leave it as is