📚 Algebra 7: Algebraic Fractions & Changing the Subject | 代数第七单元：代数分式与换元
Algebra 7 in the Edexcel IGCSE Mathematics syllabus focuses on two powerful skills: working confidently with algebraic fractions and rearranging formulas to change the subject. These skills are essential for solving equations, modelling real-world problems, and progressing to more advanced topics such as differentiation and integration.
Edexcel IGCSE 数学大纲的 Algebra 7（代数第七单元）聚焦两个核心技能：熟练处理代数分式，以及通过重排公式来更换主项。这两项技能对于解方程、建模现实问题，以及进阶到微分和积分等高阶内容都至关重要。
1. Simplifying Algebraic Fractions | 化简代数分式
An algebraic fraction has a variable in its numerator or denominator. To simplify it, you must factorise the numerator and denominator first, then cancel any common factors. Cancelling before factorising is a common mistake, so always look for factors of the full expression.
代数分式是指分子或分母中含有变量的分数。要化简它，你必须先对分子和分母进行因式分解，然后消去公因子。不因式分解就直接约分是常见错误，因此务必先寻找整个表达式的因式。
Example 1: Simplify (x² – 4) / (x² – 2x).
示例 1：化简 (x² – 4) / (x² – 2x)。
(x² – 4) / (x² – 2x) = (x – 2)(x + 2) / x(x – 2) = (x + 2) / x
Here the common factor (x – 2) is cancelled. Note that x cannot be 0 or 2 in the original fraction, because the denominator would be zero.
这里公因子 (x – 2) 被约去。注意原分式中 x 不能为 0 或 2，否则分母为零。
- Difference of two squares: a² – b² = (a – b)(a + b)
- 平方差公式：a² – b² = (a – b)(a + b)
- Quadratic factorisation: x² + 5x + 6 = (x + 2)(
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