Solving Rational Equations

This video tutorial demonstrates a method for solving rational equations by finding a common denominator, rewriting fractions, clearing fractions from the equation, and solving the simplified equation. The solution is verified by substituting back into the original equation.

What is the first step in the new method for solving rational equations?

• Add all fractions together

• Subtract the smallest fraction from the largest

• Find a common denominator for all terms

• Multiply all terms by the largest denominator

What is the least common denominator for the denominators 3, 4, 6, 2, and 12?

• 6

• 24

• 18

• 12

How do you rewrite the fraction 2/3 with a denominator of 12?

• 10/12

• 4/12

• 6/12

• 8/12

What operation is performed after rewriting all fractions with the common denominator?

• Add all fractions together

• Multiply each term by the common denominator

• Subtract the smallest fraction from the largest

• Divide each term by the common denominator

What is the purpose of obtaining a common denominator in this method?

• To divide terms equally

• To simplify multiplication

• To clear fractions from the equation

• To make addition easier

What is the result of combining like terms 8X and -2X?

• 0X

• 10X

• 6X

• 4X

What is the simplified solution for the equation after solving?

• X = 5/6

• X = 2/3

• X = 3/4

• X = 1/2

What should be done to verify the solution of the equation?

• Multiply the solution by the common denominator

• Add the solution to the original equation

• Divide the solution by the common denominator

• Substitute the solution back into the original equation

What is the result of substituting X = 2/3 back into the equation?

• The equation is not satisfied

• The solution is incorrect

• The equation is satisfied

• The solution needs to be adjusted

What is the final step in verifying the solution?

• Subtract the solution from both sides

• Add the solution to both sides

• Multiply the solution by the original denominators

• Check if the left side equals the right side