Solution of Rational Equations.

By working on this lesson you will learn how to simplify rational equations, how to get the Least Common Denominator, and to solve rational equations. The lesson presents an example followed by a companion suggested problem. You have the option to use the MARKER TOOLS menu and the pen it provides to work the problem right there in the screen or skip it and continue with the lesson using the thumbnail navigation panel at the left. Important to highlight that you may review the vocabulary provided at the bottom of the page before you go over the lesson itself. To be rational won't have to be or not to be anymore! This lesson will be expanded in the near future.

Lesson's Content

Lesson In PDF Format (no animations)


Lesson's Glossary

Equation: A mathematical statement that has to expressions joined by the = sign. It has the right side of the equation (expression1) and the left side of the equation (expression 2)

Equivalent equations: An equation that when solved have the same solution set over a given domain.

Equivalent expressions:  All expressions that represent the same number for any value of the variable that they contain.

Extraneous Solution: After an equation is solved, sometimes the number yielded in the solution doesn’t work for the original equation. This is an extraneous solution. Rational, radical, logarigthmic and absolute value equations need to be verified for this kind of solutions.

LCM: The least common multiple (LCM) of two numbers is the smallest number (different to zero) which is a multiple of both (all).

Rational expression: An expression with fractions, especially when there is a variable in the denominator. The variable can not make the denominator equal to zero

Rational function: A rational function is a function of the form f(x) = P(x)/Q(x), where P(x) and Q(x) are polynomial functions and Q(x) different than 0.

Sides of an equation:  The two expressions at both sides of the equal sign in an equation. Left and right.

Sides of an inequality: The two expressions at both sides of the inequality sign in an inequality. Left and right.

Solve an equation:  To find the solution, to find the answer, to get to know the value for which a variable stands for.

Term: A form of grouping one or more numerical and/or variable factors by means of multiplication and division. 

Variable: A letter used to represent a number. When the variable is part of an equation, it is possible to find the value for which it stands for by solving the equation. This is the solution (s) of the equation.

Variable expression: Any expression containing one or more variables.


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