Question

已知a/b=c/d,求证:(3a+2c)/(3a-2c)=(3b+2d)/(3b-2d)

Answer 1

∵a/b＝c/d,∴a/c＝b/d,∴3a/（2c）＝3b/（2d）,∴3a/（2c）＋1＝3b/（2d）＋1,

∴（3a＋2c）/（2c）＝（3b＋2d）/（2d）.······①

∵3a/（2c）＝3b/（2d）,∴3a/（2c）－1＝3b/（2d）－1,

∴（3a－2c）/（2c）＝（3b－2d）/（2d）.······②

①÷②,得：（3a＋2c）/（3a－2c）＝（3b＋2d）/（3b－2d）.