## MTE 7 - Rational Expressions and Equations

### Course Description

Effective: 2012-01-01

Includes simplifying rational algebraic expressions, solving rational algebraic equations and solving applications that use rational algebraic equations. Credit is not applicable toward graduation.
Lecture 1 hour per week.
1 credits

### General Course Purpose

The purpose of this course is to develop competency necessary to succeed in 100-level math courses in solving applications using rational algebraic equations.

### Course Prerequisites/Corequisites

Prerequisites: MTE 6 or qualifying placement score.

### Course Objectives

• Identify a rational algebraic expression.
• Identify the real value of the variable for which a rational algebraic expression having a denominator of the formax + b is undefined.
• Identify all real values of the variable for which a rational algebraic expression having a denominator of the form ax2 + bx + c is undefined.
• Express a rational algebraic expression having negative exponents as an equivalent rational expression without negative exponents.
• Simplify rational algebraic expressions.
• Simplify a rational algebraic expression.
• Evaluate a rational algebraic expression given specific integral values for each variable.
• Perform arithmetic operations with rational algebraic expressions.
• Perform addition and subtraction of rational algebraic expressions having like denominators.
• Find the Least Common Denominator (LCD) of two or more rational algebraic expressions.
• Perform addition and subtraction of rational algebraic expressions having denominators that have no common factors.
• Perform addition and subtraction of rational algebraic expressions having denominators that have a common monomial factor.
• Perform addition and subtraction of rational algebraic expressions having denominators that have a common binomial factor.
• Perform multiplication of rational algebraic expressions and express the product in simplest terms.
• Use factorization to divide rational algebraic expressions and express the quotient in simplest terms.
• Simplify complex fractions.
• Divide a polynomial by a monomial.
• Perform polynomial long division having binomial divisors of the form ax+b.
• Solve rational algebraic equations.
• Solve application problems using rational algebraic equations.
• Write a rational equation to match the information given in an application problem.
• Solve an application problem using rational equations.

### Major Topics to be Included

• Identifying a rational algebraic expression.
• Simplifying rational algebraic expressions.
• Performing arithmetic operations with rational algebraic expressions.
• Solving rational algebraic equations.
• Solving application problems using rational algebraic equations.

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