AAC #7 Rational Expressions and Equations

What is the process for subtracting rational expressions?

• 1. Find a common denominator. 2. Rewrite each fraction. 3. Subtract the numerators and keep the common denominator.

• 1. Multiply the denominators. 2. Add the numerators. 3. Simplify the result.

• 1. Find the least common multiple of the denominators. 2. Rewrite each fraction. 3. Add the numerators and keep the common denominator.

• 1. Subtract the denominators. 2. Rewrite each fraction. 3. Subtract the numerators and keep the new denominator.

What does it mean to 'simplify' a rational expression?

• To reduce the expression to its simplest form by canceling common factors.

• To multiply the expression by a common denominator.

• To add the numerator and denominator together.

• To convert the expression into a decimal form.

What is the formula for adding rational expressions with different denominators?

• Multiply the numerators and denominators together.

• Find a common denominator, rewrite each fraction, then add the numerators.

• Add the numerators directly without changing the denominators.

• Subtract the denominators and keep the numerators the same.

What is a rational expression?

• A fraction where the numerator and the denominator are both polynomials.

• A type of irrational number that cannot be expressed as a fraction.

• A polynomial equation that has no solutions.

• A mathematical expression that includes square roots of negative numbers.

How do you add rational expressions with the same denominator?

• Add the numerators together and keep the same denominator.

• Multiply the denominators and add the numerators.

• Keep the numerators the same and add the denominators.

• Subtract the numerators and keep the same denominator.

What is the first step in simplifying a complex rational expression?

• Factor both the numerator and the denominator.

• Multiply both the numerator and the denominator by the least common denominator.

• Add the numerator and the denominator together.

• Cancel out any common factors in the numerator and denominator.

What is the importance of finding a common denominator?

• A common denominator allows you to combine fractions by ensuring they are expressed in the same terms.

• A common denominator is necessary for adding whole numbers only.

• A common denominator helps in simplifying fractions to their lowest terms.

• A common denominator is used to convert fractions into percentages.

What are excluded values in rational expressions?

• Values of the variable that make the denominator zero, as they are not allowed in rational expressions.

• Values that are always positive in rational expressions.

• Values that can be any real number in rational expressions.

• Values that simplify the expression to a constant.

How do you find excluded values

• Set the numerator equal to zero

• Set the denominator equal to zero

• Find the square root of the denominator

• Evaluate the function at critical points

How do you determine if a rational expression is in simplest form?

• Check if the numerator and denominator have any common factors other than 1.

• Ensure that the numerator is greater than the denominator.

• Verify that the expression cannot be factored further.

• Confirm that the expression has no variables.