Rational Expressions and Simplification

What is the first step when you encounter rational expressions with different denominators?

• Add the numerators directly.

• Find a common denominator.

• Multiply the expressions.

• Ignore the denominators.

What should a common denominator be divisible by?

• Only the first denominator.

• Neither of the denominators.

• Both denominators.

• Only the second denominator.

Why is it important to rewrite expressions with a common denominator?

• To change the values of the expressions.

• To make the numerators equal.

• To simplify the expressions.

• To ensure the denominators are the same for subtraction.

What operation is performed on the numerators after finding a common denominator?

• Multiplication

• Subtraction

• Division

• Addition

What is the result of distributing negative z to the third across the terms?

• Positive z to the fourth and positive 6z to the third

• Positive z to the fourth and negative 6z to the third

• Negative z to the fourth and negative 6z to the third

• Negative z to the fourth and positive 6z to the third

What happens when you multiply the denominator by a new factor?

• The expression becomes undefined.

• The denominator becomes zero.

• The numerator must also be multiplied by the same factor.

• The numerator remains unchanged.

Why can't the expression be simplified further in this example?

• The terms are already in simplest form.

• The terms have different degrees.

• The numerators are not equal.

• The denominators are not equal.

What is the role of the negative sign in the subtraction process?

• It is ignored.

• It is multiplied by the denominator.

• It is added to the denominator.

• It is distributed across the numerator.

What should you do if you encounter terms with the same degree during simplification?

• Ignore them.

• Divide them.

• Multiply them.

• Add or subtract them.

What is the final step after finding a common denominator and adjusting the numerators?

• Multiply the entire expression by zero.

• Check if further simplification is possible.

• Divide the expression by the numerator.

• Add a new term to the expression.