Solving A Rational Equation With A Twist
A fast-paced walkthrough of solving (x+3)/(x-2)=2, showing each algebraic step animated in real time: clearing the denominator, expanding, and isolating x to get x=7. The video then tests understanding further by asking whether x=2 could also work, revealing why it creates division by zero and must be excluded. Useful for students practicing rational equations and recognizing extraneous solutions.
Narrated · 16:9 · Preview before teaching · automatic layout checks do not establish subject accuracy
The prompt that made it
Create a premium 60-second promotional video for TM Math Studio, an online mathematics academy for high-school students in the USA. The video should feel modern, cinematic, interactive and exciting, not like PowerPoint or a traditional classroom lecture. Do not use a talking avatar or a teacher speaking to a whiteboard. Start immediately with a dark clean mathematical background. Do not show the TM Math Studio logo at the beginning. Show the equation (x + 3) / (x - 2) = 2 in large clear mathematical text. Show the words CAN YOU SOLVE THIS? and then BEFORE THE TIMER ENDS? Start a dramatic countdown from 5 to 3. Voiceover: "Can you solve this before the timer runs out?" Next show PAUSE AND SOLVE with a short countdown from 3 to 1. Give the viewer a genuine moment to solve the problem. Do not reveal the answer yet. Voiceover: "Don't just watch. Try it. Got your answer?" Then solve the equation using smooth mathematical animation. Show (x + 3) / (x - 2) = 2 changing into x + 3 = 2(x - 2), then x + 3 = 2x - 4, then 7 = x, and finally x = 7. Animate the mathematical operations instead of simply displaying static steps. Highlight the changing parts of the equation. Voiceover: "First, clear the denominator. Then expand. Now move the x terms. And there it is. x equals 7." Then create a surprise moment with the words BUT WAIT. Return to the original equation and ask COULD x = 2? Show that when x equals 2, the denominator x - 2 becomes zero. Explain visually that division by zero is not allowed. Show x = 7 with a check mark and x = 2 with an X. Voiceover: "But there's one more thing. What if x equals 2? We can't divide by zero. So x equals 2 is not allowed." Now reveal TM Math Studio for the first time. Show beautiful mathematical animations including a moving parabola, a triangle being constructed, a rotating unit circle, a tangent line moving along a curve, algebraic expressions transforming, and a graph changing as a coefficient changes. Display the words SEE IT, UNDERSTAND IT, SOLVE IT, MASTER IT. Voiceover: "This is how we teach at TM Math Studio. We don't want students to simply memorize steps. We want them to see the mathematics, understand why it works, and learn how to solve it." Show a premium online learning environment with visual mathematics, interactive problem solving, live classes, practice challenges, Algebra, Geometry, Trigonometry, Calculus and SAT-style questions. Voiceover: "If you want math to make more sense, not just take more notes, come experience a class." For the final five seconds, show TM MATH STUDIO prominently. Then show FREE LIVE MATH DEMO. Below it show TAKE THE CHALLENGE. EXPERIENCE THE CLASS. SEE HOW WE TEACH. End with a button-style graphic saying RESERVE YOUR FREE DEMO. Final tagline: DON'T JUST MEMORIZE MATH. UNDERSTAND IT. Voiceover: "Reserve your free live math demo and experience TM Math Studio." Use a confident, friendly, intelligent and natural teacher voice. Use modern cinematic educational music with subtle tension during the countdown and a satisfying sound when x = 7 appears. Keep text short and large. Change the visual composition every few seconds. Make all mathematical equations accurate and readable. Create the video in 16:9 landscape and keep important content centered so it can later be adapted to 9:16 vertical video.
Make the next one in this series
- Show a rational equation with two extraneous solutions and how to check each one
- Animate why domain restrictions matter before solving any rational equation
- Compare solving rational equations algebraically versus graphically to find intersections
