select the correct answer. solve the rational equation.

Lyra Rowan

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29-09-2024

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Solving Rational Equations: A Step-by-Step 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:

1. Find the Least Common Multiple (LCM):

   • The LCM of the denominators (x - 1) and 1 is (x - 1).

2. 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

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 step-by-step 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.