Solving Rational Equations: A StepbyStep Guide
Rational equations are equations that contain fractions where the numerator and/or denominator involve variables. Solving these equations can be tricky, but with a systematic approach, you can master them.
Let's take a look at a common example and break down the process:
Example: Solve the following rational equation: (x + 2) / (x  1) = 3
Solution:

Find the Least Common Multiple (LCM):
 The LCM of the denominators (x  1) and 1 is (x  1).

Multiply both sides of the equation by the LCM:
 (x  1) * [(x + 2) / (x  1)] = 3 * (x  1)
 This simplifies to x + 2 = 3x  3

Solve for x:
 Subtract x from both sides: 2 = 2x  3
 Add 3 to both sides: 5 = 2x
 Divide both sides by 2: x = 5/2
Therefore, the solution to the rational equation (x + 2) / (x  1) = 3 is x = 5/2.
Important Considerations:

Extraneous Solutions: Always check your solutions by plugging them back into the original equation. Sometimes a solution you find might make a denominator zero, which is undefined. Such solutions are called extraneous solutions and must be discarded.

Using Brainly for Assistance:
 Brainly is a great resource for finding answers to specific math problems. If you're struggling with a particular step, you can search for similar questions on Brainly and use the explanations provided by other users.
 Remember to acknowledge the source when using information from Brainly. It's always a good practice to give credit to the original author.
Let's look at an example from Brainly:
 Question: Solve the following equation: x / (x  2) + 1 / (x  1) = 1 (Source: Brainly)
 Solution: The explanation on Brainly provides a stepbystep solution, similar to the one above. It starts by finding the LCM, multiplying both sides by it, and then solving for x.
Additional Tips for Solving Rational Equations:
 Simplify before multiplying: If possible, simplify the fractions in the equation before finding the LCM.
 Factor denominators: This often helps identify the LCM more easily.
 Use a calculator for complex calculations: Don't be afraid to use a calculator to help with the arithmetic if needed.
By following these steps and using resources like Brainly, you can confidently solve rational equations and tackle more complex algebraic challenges.