Solving Rational Equations: Key Concepts and Techniques

What is the least common denominator (LCD) for fractions with denominators x+5 and x-3?

• x^2+2x-15

• x+5

• x-3

• x^2-2x-15

What is the purpose of finding the LCD in equations involving fractions?

• To simplify the equation

• To make the denominators the same for easier solving

• To eliminate the fractions

• To find the highest possible denominator

When solving equations with fractions, what must be true about the denominators?

• They must be different

• They must not contain variables

• They must contain variables

• They must be the same

What is the result of solving the equation after converting fractions to have the same denominator?

• x = 5

• x = -5

• x = 3

• x = -3

Why was x = -5 considered an extraneous solution?

• It was the only solution found

• It made the denominator zero

• It did not satisfy the original equation

• It was not a real number

What symbol represents no solution?

• An empty set

• A question mark

• Infinity symbol

• A zero

What does the 'double bubble' method refer to?

• A strategy for factoring trinomials

• A technique for simplifying fractions

• A method for finding the LCD

• A way to solve quadratic equations

After factoring the trinomial y^2 + 2y - 3, what are the factors?

• y+3 and y-1

• y-3 and y-1

• y-3 and y+1

• y+3 and y+1

What are the solutions to the equation after factoring?

• y = -3 and y = 1

• y = 3 and y = -1

• y = 3 and y = 1

• y = -3 and y = -1

How do you check if a solution is extraneous?

• By drawing a graph

• By factoring the equation again

• By adding it to the equation

• By substituting it back into the original equation