Understanding Rational Equations

The video tutorial explains how to solve a rational equation by eliminating fractions using the least common denominator (LCD). It covers factoring polynomials, multiplying each term by the LCD, simplifying the equation, and solving for the variable. The tutorial also emphasizes the importance of checking solutions to ensure they do not make any denominator zero, which would be undefined.

What is the purpose of multiplying both sides of a rational equation by an expression?

• To create fractions

• To divide fractions

• To eliminate fractions

• To add fractions

What is the least common denominator (LCD) used for in solving rational equations?

• To eliminate variables

• To eliminate fractions

• To add fractions

• To find the greatest common factor

Why is it important to factor the denominators when solving rational equations?

• To simplify the numerators

• To find the least common denominator

• To add the fractions

• To eliminate the equation

What happens when you multiply each term in the equation by the LCD?

• The equation becomes more complex

• The fractions are eliminated

• The equation is divided

• The equation is unchanged

What is the result of simplifying the equation after multiplying by the LCD?

• An unchanged equation

• An equation with more fractions

• A simpler equation with no fractions

• A more complex equation

How do you solve the resulting equation after clearing the parentheses?

• By adding more terms

• By dividing all terms

• By combining like terms and setting it to zero

• By multiplying all terms

What is the next step after setting the equation to zero?

• Factoring the equation

• Adding more terms

• Dividing all terms

• Multiplying all terms

Why must we exclude certain values of x when solving rational equations?

• They make the equation too complex

• They make the denominator zero

• They simplify the equation

• They add more fractions

What value of x must be excluded because it makes the denominator zero?

• x = 5

• x = -6

• x = 1

• x = 0

What is the final solution for x in the given rational equation?

• x = 3

• x = -1

• x = 0

• x = 2