Adding and Subtracting Algebraic Fractions | 代数分式的加减法

📚 Adding and Subtracting Algebraic Fractions | 代数分式的加减法

Algebraic fractions are fractions whose numerator, denominator, or both contain algebraic expressions. Adding and subtracting them follows exactly the same logic as numerical fractions: you must first obtain a common denominator, then combine the numerators, and finally simplify the result. This skill is essential for many Edexcel IGCSE Mathematics topics, including solving rational equations, rearranging complex formulae, and working with functions.

代数分式是指分子、分母或两者中带有代数表达式的分数。它们的加减运算与数值分数的逻辑完全一致：首先必须确定公分母，然后合并分子，最后化简结果。这项技能在爱德思 IGCSE 数学中至关重要，涉及解有理方程、变形复杂公式以及处理函数等内容。

Many students treat algebraic fractions with fear because variables appear alongside numbers. In truth, the rules are identical to the ones you already know from arithmetic: the denominator tells you “how many equal parts” the numerator refers to, and you can only combine parts of the same size. When the denominators differ, you must cut each fraction into smaller equal parts by multiplying both numerator and denominator by the same factor.

许多学生因为式中含有变量而对代数分式感到畏惧。事实上，它的运算规则与你熟悉的算术完全一致：分母告诉你分子所表示的是”多少个等份”，只有等份大小相同时才能合并。当分母不同时，需要把每个分数都切成更小的等份，即把分子分母同时乘以同一个因式。

1. Why Algebraic Fractions Behave Like Number Fractions | 为什么代数分式与数值分数行为一致

Every fraction obeys one fundamental rule: two fractions can only be

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