Rational Equations and Their Solutions

The video tutorial explains how to solve a rational equation by first identifying values that make the denominator zero, which cannot be solutions. It then guides through finding the least common denominator to clear fractions, simplifying the equation, and solving for x. Finally, it suggests checking the solution by substituting it back into the original equation.

What is the first step in solving a rational equation?

• Identify values that make the denominator zero

• Solve for x

• Multiply both sides by the numerator

• Identify the least common denominator

Why can't x equal zero in the given equation?

• Because it would make the solution negative

• Because it would make the numerator zero

• Because it would make the equation too complex

• Because it would make the equation undefined

What is the least common denominator in the given equation?

• 5x

• 5

• x

• x-1

What is the purpose of multiplying both sides by the least common denominator?

• To simplify the numerators

• To clear the fractions from the equation

• To solve for x directly

• To add fractions

What happens when you simplify x divided by x in the equation?

• It becomes undefined

• It becomes one

• It becomes x

• It becomes zero

What is the result of distributing 5 in the equation?

• 5x + 5 + 3x = 10

• 5x - 5 - 3x = 10

• 5x + 5 - 3x = 10

• 5x - 5 + 3x = 10

How do you isolate 2x in the equation?

• Divide both sides by 2

• Subtract 5 from both sides

• Add 5 to both sides

• Multiply both sides by 2

What is the solution to the equation after isolating x?

• x = 10

• x = 5

• x = 15

• x = 15/2

What is the final step to verify the solution?

• Multiply the solution by the denominator

• Add the solution to the numerator

• Divide the solution by the denominator

• Substitute the solution back into the original equation

Why is it important to check the solution in the original equation?

• To confirm the solution does not make the denominator zero

• To check if the solution is greater than zero

• To verify the solution is a whole number

• To ensure the solution is positive