Simplifying Rational Expressions: Adding and Subtracting

What is the first step in simplifying a non-factored rational expression?

• Factor the numerator and denominator completely

• Divide the numerator by the denominator

• Identify the non-permissible values

• Simplify the expression to its lowest terms

What must be done before simplifying the rational expression by dividing common factors?

• Multiply the numerator and denominator

• State the non-permissible values

• Subtract the common factors

• Add the numerator to the denominator

Which method involves breaking down the middle term to factor a quadratic expression?

• Synthetic division

• Rational root theorem

• Completing the square

• Decomposition

In the guess and check model of factoring, what is crucial to find?

• Pairs of numbers that sum to the middle coefficient

• The highest common factor

• The discriminant

• The roots of the equation

What is the result of simplifying the expression with a common factor in the numerator and denominator?

• The difference of the two factors

• The quotient of the two factors

• The sum of the two factors

• The product of the two factors

What should be done when the terms in the numerator and denominator are exact opposites?

• Leave them as they are

• Multiply them

• Factor out negative one from one of the terms

• Add them together

How can non-permissible values affect the simplification of rational expressions?

• They determine the highest common factor

• They indicate values that make the denominator zero

• They simplify the expression directly

• They are used to multiply the factors

What is the simplest form of an expression where the numerator and denominator share a common binomial factor?

• The binomial factor itself

• The quotient of the non-common parts

• The product of the common factor and the highest coefficient

• The sum of the coefficients

When dealing with a rational expression involving two variables, what must be considered for simplification?

• The difference between the variables

• The relationship between the variables that makes the denominator zero

• The product of the variables

• The sum of the variables

What technique is used to simplify expressions where factors are exact opposites?

• Factoring out negative one

• Applying the quadratic formula

• Using synthetic division

• Solving a system of equations