Rational Equations and Their Solutions

The video tutorial explains how to solve rational equations by multiplying both sides by the least common denominator (LCD) to eliminate denominators. It covers factoring denominators, identifying the LCD, and solving the resulting equation. The tutorial also emphasizes checking for valid solutions to avoid division by zero.

What is the first step in solving a rational equation?

• Multiply both sides by the least common denominator

• Add the numerators

• Divide by the greatest common factor

• Subtract the denominators

How do you factor the expression x^2 - 4?

• (x + 2)(x + 2)

• (x - 2)(x - 2)

• (x + 2)(x - 2)

• (x - 4)(x + 4)

What is the least common denominator of x - 2 and x^2 - 4?

• x + 2

• x^2 - 4

• x - 2

• (x + 2)(x - 2)

What is the purpose of multiplying each fraction by the LCD?

• To simplify the numerators

• To increase the equation's complexity

• To eliminate the denominators

• To find a common numerator

What happens to the equation after multiplying by the LCD?

• It becomes a fraction

• It becomes a polynomial

• It becomes a rational expression

• It becomes a logarithmic equation

After eliminating the denominators, what type of equation do we solve?

• Cubic equation

• Quadratic equation

• Linear equation

• Exponential equation

What is the result of simplifying x^2 + 2x + x?

• 3x^2 + x

• x^2 + x

• x^2 + 3x

• x^2 + 2x

What is the final solution for x in the equation?

• x = 3

• x = -3

• x = 2

• x = -2

What should you check for after solving a rational equation?

• If the solution is less than zero

• If the solution is a whole number

• If the solution is positive

• If the solution causes division by zero

Which values of x must be excluded to avoid division by zero?

• x = 1

• x = 0

• x = 3

• x = 2 and x = -2