Up to this point, all of the possible solutions have solved the original equation. However, this may not always be the case. Multiplying both sides of an equation by variable factors may lead to extraneous solutions, which are solutions that do not solve the original equation. A complete list of steps for solving a rational equation is outlined in the following example.
Example 3: Solve:
x
x
+
2
+
2
x
2
+
5
x
+
6
=
5
x
+
3
.
Solution:
Step 1: Factor all denominators and determine the LCD.
Answers & Comments
Answer:
The solutions are −1/2 and 1.
Up to this point, all of the possible solutions have solved the original equation. However, this may not always be the case. Multiplying both sides of an equation by variable factors may lead to extraneous solutions, which are solutions that do not solve the original equation. A complete list of steps for solving a rational equation is outlined in the following example.
Example 3: Solve:
x
x
+
2
+
2
x
2
+
5
x
+
6
=
5
x
+
3
.
Solution:
Step 1: Factor all denominators and determine the LCD.
Step-by-step explanation: