Solving a rational Equation

The video tutorial explains how to solve a rational equation by eliminating fractions through finding the least common denominator (LCD). It demonstrates multiplying each term by the LCD to remove denominators, applying the distributive property, and solving the resulting quadratic equation. The tutorial also covers factoring the quadratic equation and checking for extraneous solutions to ensure they satisfy the original equation.

What is the purpose of finding the least common denominator (LCD) in solving rational equations?

• To solve for the variable directly

• To find the greatest common factor

• To eliminate the fractions

• To simplify the numerators

When multiplying each term by the LCD, what property is applied to ensure the equation remains balanced?

• Commutative property

• Identity property

• Associative property

• Distributive property

After simplifying the equation, what type of equation is formed that needs to be solved?

• Quadratic equation

• Linear equation

• Rational equation

• Exponential equation

Which method is used to solve the quadratic equation obtained from the rational equation?

• Factoring

• Graphing

• Completing the square

• Using the quadratic formula

Why is it important to check the solutions of the quadratic equation in the context of the original rational equation?

• To confirm the solutions are integers

• To ensure the solutions are positive

• To verify the solutions are not extraneous

• To check if the solutions are complex numbers