Exploring Adding and Subtracting Rational Expressions

What is the first step in solving rational equations using proportions?

• Distribute the terms

• Cross multiply

• Find the least common denominator

• Factor the equation

How do you write the solution for x = -8 in set notation?

• [x = -8]

• (-8)

• {-8}

• x = {-8}

What method involves multiplying each side of the equation by the least common denominator?

• Using the LCD

• Using proportions

• Factoring

• Cross multiplication

What is the result of cross multiplying 3/a - 8 = 7/(2a + 1)?

• 3a - 8 = 14a + 7

• 3(2a + 1) = 7(a - 8)

• 21a - 8 = 2a + 1

• 6a + 3 = 7a - 56

In solving rational equations, what does LCD stand for?

• Last Calculated Denominator

• Least Common Denominator

• Lowest Common Denominator

• Least Common Divisor

When using the LCD method, what is the next step after identifying the least common denominator?

• Check the solution

• Cross multiply

• Multiply every term by the LCD

• Simplify the equation

When solving rational equations, why is it important to check your solutions?

• To convert the solution to set notation

• To ensure the solution fits the original equation

• To simplify the equation further

• To find additional solutions

What is the correct set notation for a solution that does not exist?

• {}

• {0}

• ∅

• [-∞,∞]

Why might a solution be excluded after checking it in the original equation?

• If it is a negative number

• If it results in division by zero

• If it simplifies to a fraction

• If it is not a whole number

What does factoring involve in the context of solving rational equations?

• Cross multiplying

• Breaking down equations into simpler forms

• Dividing by the LCD

• Multiplying terms