Mastering Rational Expressions with Like Denominators

What is the first step in adding two rational expressions with the same denominator?

• Keep the common denominator and add the numerators

• Multiply the numerators

• Subtract the numerators

• Add the denominators

How do you simplify the expression after adding the numerators?

• Factor the denominator

• Multiply the numerator by the denominator

• Divide the numerator by the denominator

• Combine like terms

What is the correct approach to adding rational expressions?

• Multiply both expressions

• Keep the denominator if it is already common and add the numerators

• None of the above

• Change the denominators to be the same

What signifies that two rational expressions can be directly added or subtracted?

• They have the same numerator

• Their denominators are different

• They have the same denominator

• Their numerators are opposites

In the expression 6 + (-3x - 8) over 2x^2 - 7, what is the simplified form of the numerator?

• -3x - 8

• -3x + 2

• 3x - 2

• -3x - 2

What is the denominator in the subtraction of two rational expressions with the same denominator?

• The common denominator

• The product of the two denominators

• The difference of the two denominators

• The sum of the two denominators

How do you handle the subtraction of the numerators in rational expressions?

• Multiply the numerators

• Distribute the negative sign and then combine like terms

• Divide the first numerator by the second

• Subtract directly across

What is the result of simplifying 9x^2 + 3 - (-3x^2 + 5)?

• 6x^2 + 8

• 6x^2 - 2

• 12x^2 + 8

• 12x^2 - 2

Can the final expression 12x^2 - 2 over 14x^2 - 9 be simplified further by factoring?

• No, because they are already in simplest form

• Yes, by dividing both by 2

• No, they are differences of squares of different things

• Yes, they have common factors

After distributing the negative sign in subtraction, what should you do next?

• Cancel out terms between the numerator and denominator

• Factor the numerator

• Simplify the denominator

• Combine like terms in the numerator