Solving Rational Equations and Identifying Extraneous Solutions

What is a rational equation?

• An equation with only one solution

• An equation with at least one rational expression

• An equation with only whole numbers

• An equation with no variables

Why is it important to check for extraneous solutions?

• To eliminate variables

• To find more solutions

• To ensure the solution is within the domain

• To simplify the equation

What is the first step in solving a proportion?

• Subtracting fractions

• Adding fractions

• Dividing fractions

• Cross-multiplying

What is the second method for solving rational equations?

• Adding fractions

• Eliminating denominators

• Cross-multiplying

• Dividing fractions

In the first example, what are the solutions to the equation x/(x-6) = 1/(x-4)?

• x = 1 and x = 5

• x = 2 and x = 4

• x = 4 and x = 6

• x = 3 and x = 2

What is the result of factoring x^2 - 5x + 6?

• (x-3)(x-2)

• (x+3)(x+2)

• (x+1)(x-5)

• (x-1)(x-6)

In the second example, what is the factored form of x^2 - 9?

• (x-4)(x+5)

• (x-3)(x+3)

• (x-2)(x+2)

• (x-1)(x+9)

What are the solutions to the equation x/(x-3) + x/(x+3) = 2/(x^2-9)?

• x = 4 and x = -4

• x = 2 and x = -2

• x = 1 and x = -1

• x = 3 and x = -3

In the third example, what makes -2 an extraneous solution?

• It results in a zero in the denominator

• It results in a negative number

• It results in a complex number

• It results in an undefined value

What is the final solution to the equation 2x + 2 + x/(x-2) = 1?

• x = 2

• x = -1

• x = 1

• x = 0