Equations with rational expressions (example 2) | Mathematics III | High School Math | Khan Academy

TL;DR

The video explains how to solve a rational equation by getting rid of the denominators and simplifying the equation.

Transcript

• [Voiceover] So we have a nice, little equation here that has some rational expressions in it and like always, pause the video and see if you can figure out which x's satisfy this equation. All right. Let's work through it together. Now, when I see things at the denominator like this, my instinct is to try to not have denominators like this. And s... Read More

Key Insights

• 🙃 Multiplying both sides of an equation by a common factor can help eliminate denominators.
• 🍉 Combining like terms is an essential step in solving rational equations.
• ✅ Checking the validity of solutions is crucial to avoid extraneous solutions.
• 💁 Factoring a quadratic equation can help solve the equation in factored form.

Questions & Answers

Q: How does multiplying both sides by the denominators help in solving the equation?

Multiplying both sides by the denominators eliminates them from the equation and allows us to work with simpler expressions.

Q: How are the like terms combined in the equation?

The speaker combines the terms with x on one side of the equation and the constant terms on the other side.

Q: How are the solutions found?

The solutions are found by setting each factor on the left-hand side of the equation equal to zero and solving for x.

Q: Why is it important to check if the solutions make the denominators equal to zero?

Checking if the solutions make the denominators equal to zero is important to avoid extraneous solutions that may arise from simplifying the equation.

Summary & Key Takeaways

• The speaker suggests multiplying both sides of the equation by the denominators to eliminate them.

• After simplifying the equation, they combine like terms and solve for x.

• Two solutions are found, and it is ensured that neither of them makes any of the denominators equal to zero.