Rút gọn biểu thức chứa căn

Overview

A step‑by‑step visual derivation of the simplification of the expression
$$A = \frac{2x + 3\sqrt{x} - 8}{(\sqrt{x}-1)(\sqrt{x}+2)} - \frac{\sqrt{x}-2}{\sqrt{x}-1} + \frac{2}{\sqrt{x}+2}$$
for $x\ge 0,\; x eq 1$. The key takeaway is the final reduced form $A = \frac{\sqrt{x}+6}{\sqrt{x}+2}$.

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Phases

#	Phase Name	Duration	Description
1	Title & Problem	~5 s	Title appears at the top, subtitle fades in, then the full problem statement with domain condition is written and held.
2	Step 1 – Common denominator	~6 s	Label "Bước 1: Quy đồng mẫu thức chung" slides in from the left, followed by the combined‑fraction form of $A$.
3	Step 2 – Expand numerator	~9 s	Label "Bước 2: Khai triển và thu gọn tử thức" appears, then three successive equations are shown: expansion, intermediate simplification, and the compact numerator $x + 5\sqrt{x} - 6$.
4	Clean‑up & reposition	~3 s	All earlier text fades out, the compact numerator moves to the top of the screen to make room for the final steps.
5	Step 3 – Factor & cancel	~8 s	Label "Bước 3: Phân tích nhân tử và rút gọn biểu thức" appears, the factored form is written, then the cancellation is performed, revealing the final simplified expression in yellow.
6	Conclusion box	~4 s	A short caption "Vậy biểu thức rút gọn là:" appears, the final expression is placed beside it, and a yellow surrounding rectangle highlights the result.
7	End pause	~3 s	Hold on the final boxed result for the viewer to absorb.

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Layout

┌─────────────────────────────────────────────┐
│                 TITLE / SUBTITLE            │
├─────────────────────────────────────────────┤
│                 MAIN (problem & steps)      │
├─────────────────────────────────────────────┤
│            Caption / result box (footer)    │
└─────────────────────────────────────────────┘

Area Descriptions

Area	Content	Notes
Title / Subtitle	Large yellow title "ĐỀ THI TUYỂN SINH VÀO LỚP 10" and blue subtitle "Bài toán rút gọn biểu thức chứa căn" placed at the top edge.	Persistent for the first two phases, then fades out.
Main	Sequential mathematical expressions for the problem statement, each step label, and the evolving equations.	Takes most of the vertical space; equations are left‑aligned for readability.
Caption / result box	Small green caption "Vậy biểu thức rút gọn là:" together with the final yellow expression, surrounded by a yellow rectangle.	Appears only in the final phase, anchored near the bottom of the frame.

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Notes

• Assumptions: No additional voice‑over or explanatory text beyond the step labels; timing is chosen for a typical classroom pacing (≈1 s per line of text, 1.5 s for transforms).
• All fades, writes, and transforms are smooth linear animations; no abrupt jumps.
• Colors follow the original code (yellow title, blue subtitle, orange step labels, green caption, yellow highlight for the final expression).
• The entire animation fits within a single Manim Scene class.
• No persistent on‑screen axes or grids are needed; the focus is purely on algebraic manipulation.
• The final rectangle is created after the final expression appears to emphasize the answer.