Adding and Subtracting Rational Expressions with Like Denominators

What is the first step in adding rational expressions with like denominators?

• Look for restrictions in the denominator

• Solve for the variable in the denominator

• Identify and simplify the denominator

• Combine like terms in the numerator

What must the denominators in rational expressions be for direct addition or subtraction?

• Quadratic expressions

• The same

• Prime numbers

• Different

How do you handle the subtraction of rational expressions?

• By adding the numerators directly

• By distributing the minus sign across the numerator

• By changing the denominator

• By multiplying both expressions

What happens to terms in the numerator that are exact opposites?

• They cancel each other out

• They double in value

• They become the denominator

• They remain unchanged

What indicates that a rational expression cannot be further simplified?

• The expression has a quadratic denominator

• There are no like terms to combine

• The denominator equals zero

• The numerator is a prime number

How do you find restrictions for rational expressions with quadratic denominators?

• By factoring the denominator

• By setting the denominator equal to zero

• By simplifying the numerator

• By using the quadratic formula

What does a negative discriminant in the quadratic formula indicate?

• Two real solutions

• One real solution

• Imaginary solutions

• No real solutions

When subtracting rational expressions, why is it important to distribute the negative sign?

• To ensure accurate subtraction of terms

• To correctly combine like terms

• To simplify the denominator

• To identify restrictions

What is the result of factoring x^2 - 2x - 8?

• Cannot be factored

• x - 4 and x - 2

• x + 4 and x - 2

• x - 4 and x + 2

What are the restrictions for the expression with a denominator of x^2 - 2x - 8?

• x cannot be 4 or -2

• x cannot be 4 or 2

• There are no restrictions

• x cannot be -4 or 2