Chapter 1
Linear Equations and Graphing
Course: Gre
Subject: Gre Quantitative Reasoning
Chapter: Rational Expressions And Equations
Introduction: What Is a Rational Equation?
A rational equation is an equation that contains one or more rational expressions—fractions where the numerator and denominator are polynomials. The defining feature of a rational equation is the presence of a variable in the denominator.
2(x-9)x+5x=-4x+5x
In this equation, the variable xappears in the denominator, making it a rational equation.
Rational Equation vs. Rational Expression
The distinction between a rational equation and a rational expression is simple:
| Type | Definition | Example | | Rational Expression | A fraction with polynomials; no equals sign | x2+x2x2-3x+4 | | Rational Equation | An equation where one or more terms are rational expressions | x2+x2x2-3x+1=x2x-1 |
If an equals sign is present, it is an equation. If not, it is an expression.
Steps for Solving Rational Equations