Solving Rational Equation with Whole Number - Part 2 - General Mathematics

Summary

In this educational video, Ton teaches viewers how to solve rational equations with whole numbers. He starts by identifying the least common denominator (LCD) and restricted value (RV), which is crucial to avoid undefined expressions. The LCD in this case is x-5. He then demonstrates the process of eliminating the denominator by multiplying the entire equation by the LCD, leading to a simplified equation. After solving, he finds x=15, and checks the solution by substituting back into the original equation. The video concludes with a reminder to like, subscribe, and turn on notifications for more informative content.

Takeaways

• 📘 The video focuses on solving rational equations, specifically one involving a whole number.
• 🔍 The key to solving rational equations is eliminating the denominator.
• 🌟 The LCD (Least Common Denominator) for the given equation is (x - 5).
• ⚠️ The Restricted Value (RV) is x = 5, as this makes the denominator zero, resulting in an undefined expression.
• 📖 The process involves multiplying the entire equation by the LCD to eliminate the denominators.
• 🔢 After multiplying, the equation simplifies to 3x = 5x - 25.
• 🧮 Transposing terms leads to 2x = 30, which simplifies to x = 15.
• 📝 The solution set is x = 15, which is the value that satisfies the original equation.
• 🔄 To verify the solution, substitute x = 15 back into the original equation and check for equality on both sides.
• 📢 The presenter encourages viewers to like, subscribe, and turn on notifications for updates.

Q & A

What is the main topic of the video?

The main topic of the video is solving rational equations, specifically focusing on how to eliminate the denominator in a rational equation.

What is the given rational equation in the video?

The given rational equation is \(\frac{3x}{x-5} = \frac{5}{x-5}\).

What is the LCD (Least Common Denominator) for the equation presented?

The LCD for the given equation is \(x-5\), as it is the common denominator present in both fractions.

What is a Restricted Value (RV) in the context of the video?

A Restricted Value (RV) is a value that makes the denominator of a fraction equal to zero, which would make the fraction undefined. In this case, the RV is 5 because \(x-5 = 0\) when \(x = 5\).

How does the video suggest eliminating the denominator?

The video suggests eliminating the denominator by multiplying the entire equation by the LCD, which is \(x-5\) in this case.

What is the simplified form of the numerator after eliminating the denominator?

After eliminating the denominator, the numerator simplifies to \(3x\) on the left side and \(5x - 25\) on the right side.

How is the value of x found in the video?

The value of x is found by simplifying the equation to \(3x = 5x - 25\), then isolating x by subtracting \(3x\) from both sides to get \(2x = 30\), and finally dividing by 2 to find \(x = 15\).

What is the solution set for the rational equation according to the video?

The solution set for the rational equation is \(x = 15\).

How does the video suggest checking the solution?

The video suggests checking the solution by substituting \(x = 15\) back into the original equation to see if both sides are equal.

What is the result of checking the solution in the video?

Upon checking, the video confirms that substituting \(x = 15\) into the original equation results in both sides being equal, verifying that the solution is correct.

What is the final advice given by the presenter at the end of the video?

The presenter advises viewers who are new to the channel to like, subscribe, and enable notifications to stay updated with the latest uploads.