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:
Isolate the terms with variable on one side and constants on the other side
Add or subtract terms with variable
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:
What is the value of if ?
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:
If what is a possible value of ?
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: