6e)++Solving+rational+equations

First, what is a rational equation? Well, a rational number is any number that can be expressed as a fraction or ratio and an equation is any two expressions separated by an equal sign. Rational equations are very similar to solving regular equalities. When each side of the equation is a single rational expression, you can cross multiply them to find the answer. However, when each side does not have one single rational expression, you have to multiply each side of the equation by the least common denominator (LCD). After this you have to simplify the problem and then check the solution. There can either be 2, 1, or 0 answers to a rational equation. In order to find out how many answers there are, after you solve you always have to check for extraneous solutions. Before you do anything, you need to be aware that in this problem x cannot equal -2 or o because that would make the denominators equal to zero. When you finish the problem you need to make sure that the solutions do not equal these numbers because that would make them extraneous.
 * This section will teach you how to solve rational equations.**

This is an example of an equation that does not have a single rational expression on both sides of the equal sign, and therefore you need to find the LCD in order to solve. The LCD of this equation would be 5x(x+2). In order to solve the problem you must multiply whole sides both sides by the LCD 5x(x+2) and after you finish the problem you must check your answers to make sure that your solution is not extraneous.

3 examples on solving rational equations:
** 
 * __Example 1:__
 * Check:**

Yes, this answer checks!


 * __Example 2:__


 * LCD for 3x, 4, and x: 12x





Check:** Yes, it Checks!


 * __Example 3:__**

3(x+8) = 15(x+1) 3x + 24 = 15x + 15 -12x = -9
 * x=3/4**


 * Check:**

3(.75+8)=15(.75+1) 3(8.75) = 15(1.75) 26.25 = 26.25
 * Yes, it checks!**

__Helpful Links:__ [|Purple Math] [|CliffsNotes]

Textbook: 8.6 //Solve Rational Equations// (Page 589 - 606)