Solving Rational Equations

The video tutorial discusses solving rational equations, starting with a brief overview of rational expressions and the importance of the denominator not being zero. It then demonstrates two methods for solving rational equations: cross multiplication and using the least common denominator (LCD). The tutorial provides step-by-step solutions to example problems and encourages viewers to practice solving a given equation using the discussed methods.

What is a rational expression?

• An expression with a variable in the numerator

• An expression written as a fraction with a non-zero denominator

• An expression with a variable in the denominator

• An expression that equals zero

Why must the denominator in a rational expression not be zero?

• It results in an undefined expression

• It makes the expression equal to one

• It makes the expression negative

• It simplifies the expression

What is the first step in solving a rational equation using cross multiplication?

• Add the numerators

• Cross multiply the terms

• Multiply the denominators

• Subtract the numerators

In the equation 1/x = 2/(3x-1), what do you get after cross multiplying?

• x = 2x

• 3x - 1 = 2x

• 3x = 2x

• x - 1 = 2x

What is the alternative method to solve rational equations besides cross multiplication?

• Using substitution

• Using the least common denominator (LCD)

• Using addition

• Using division

What is the LCD of the equation 1/x - 2/(3x-1) = 0?

• x

• 3x - 1

• x(3x - 1)

• 1

After finding the LCD, what is the next step in solving the equation?

• Subtract the numerators

• Multiply the entire equation by the LCD

• Add the numerators

• Divide by the LCD

What is the solution to the equation 1/x = 2/(3x-1) using the LCD method?

• x = 0

• x = 1

• x = -1

• x = 2

Which method is generally easier for solving rational equations?

• Cross multiplication

• Using the LCD

• Substitution

• Graphing

What is the first step in solving the equation (x-2)/(2x+4) = 1/5?

• Add 2 to both sides

• Cross multiply

• Find the LCD

• Subtract 1 from both sides