## 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.