Rewriting Rational Expressions Using Long Division and Remainders

The video tutorial teaches how to rewrite rational expressions using long division and remainders. It begins with an introduction to rational expressions and the concept of a plus b over c form. The tutorial explains how to decompose fractions and handle variables in expressions. A step-by-step example of long division with variables is provided, demonstrating how to rewrite expressions and identify remainders. The tutorial concludes with a summary of the process and key points to remember.

What is the a + b/c form used for in rational expressions?

• To find the greatest common factor

• To convert fractions to decimals

• To multiply fractions

• To express a fraction as a sum of a whole number and a fraction

How should you treat the variable 'x' in rational expressions?

• As an unknown number similar to a placeholder

• As a constant number

• As a fraction

• As a decimal

What is the first step in rewriting a rational expression using long division?

• Add the numerator and the denominator

• Divide the numerator by the denominator

• Rewrite the expression in a + b/c form

• Multiply the numerator by the denominator

In the example provided, what is the remainder when dividing 3x squared minus 4x plus 15 by x plus 7?

• 25

• 15

• 90

• 190

Why is it important to ensure that the denominator does not equal zero?

• It makes the expression a whole number

• It simplifies the expression

• It changes the value of the expression

• It makes the expression undefined