Sunday, July 14, 2013

10:50 AM
The equations that have variables in the denominator are termed as rational equations. Even though this may be a new name for you, it uses the same concepts used in solving regular algebra equations.
Here are some e xamples of rational equations:

To solve rational equations, you should first convert them into a standard linear or quadratic form. This can be done using one or more of the following steps. Usually the simpler rational equations may not involve all of these steps:
  1. Isolate the terms with variable on one side and constants on the other side
  2. Add or subtract terms with variable
  3. Cross-multiply both sides to get a standard linear or quadratic equation
Let’s take an example involving a simple rational equation that converts to a linear form:
Example:

What is the value of   if ?
A) 1
B) 2
C) 3
D) 4
E) 5
Solution:

Step 1: Here we see that all variable terms are already on one side. Therefore we first use the cross-multiplication to simplify the equation:
Step 2: Next we get rid of the parentheses:
Step 3: Finally isolate the variable to solve the equation
D is the correct answer.

Sometimes you can also simplify the equation into a linear or quadratic form a lot quicker by multiplying both sides of the equation with the denominator containing the variable term. Let’s look at a grid-in example:
Example:

If   what is a possible value of ?
Solution:

This question can be easily solved by plugging in the values if you have the luxury of answer choices. But alas! This seems to be a fill in the blank type of question. Sadly you will have to solve this question using math concepts.
Step 1: To solve the question we need to eliminate the  in the denominator. This can be done by multiplying both sides of the equation by 
Step 2: The next step is to factorize the quadratic equation:
Either 1 or 2 could be the correct answer.

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