{"id":69,"date":"2026-05-16T00:15:39","date_gmt":"2026-05-15T16:15:39","guid":{"rendered":"https:\/\/done.baka233.top\/?p=69"},"modified":"2026-05-16T00:21:40","modified_gmt":"2026-05-15T16:21:40","slug":"%e5%85%b3%e4%ba%8e%e5%a2%9e%e6%a0%b9","status":"publish","type":"post","link":"https:\/\/done.baka233.top\/index.php\/2026\/05\/16\/%e5%85%b3%e4%ba%8e%e5%a2%9e%e6%a0%b9\/","title":{"rendered":"\u5173\u4e8e\u589e\u6839"},"content":{"rendered":"<h3>\u524d\u8a00<\/h3>\n<p>\u5728\u5b66\u4e60\u5206\u5f0f\u65b9\u7a0b\u65f6\uff0c\u6211\u4eec\u4f1a\u521d\u6b21\u63a5\u89e6\u5230\u201c\u589e\u6839\u201d\u8fd9\u4e2a\u6982\u5ff5\u3002\u6211\u8fd9\u8fb9\u7528\u7684\u5317\u5e08\u5927\u7248\u6559\u6750\u4e0a\u5bf9\u4e8e\u589e\u6839\u6ca1\u6709\u8fc7\u591a\u7684\u9610\u8ff0\uff0c\u53ea\u662f\u4e3e\u4f8b\u5728\u67d0\u4e2a\u5206\u5f0f\u65b9\u7a0b\u4e2d\u89e3\u51fa\u6765\u4e00\u4e2a$x$\uff0c\u53d1\u73b0\u5b83\u4f7f\u5f97\u539f\u5206\u5f0f\u65b9\u7a0b\u5206\u6bcd\u4e3a0\uff0c\u4fbf\u79f0\u5176\u4e3a\u539f\u65b9\u7a0b\u7684\u589e\u6839\u3002\u5355\u770b\u8fd9\u4e2a\u5b9a\u4e49\uff0c\u8fd8\u86ee\u597d\u7406\u89e3\u7684\uff0c\u5c06\u8fd9\u4e2a$x$\u4ee3\u5165\u539f\u5206\u5f0f\u65b9\u7a0b\u540e\uff0c\u4f1a\u51fa\u73b0\u65e0\u610f\u4e49\u7684\u5206\u5f0f\uff0c\u81ea\u7136\u4e0d\u80fd\u7b97\u4f5c\u539f\u65b9\u7a0b\u7684\u6839\u3002\u53ef\u76f4\u5230\u6211\u9047\u5230\u4e86\u8fd9\u6837\u4e00\u9053\u9898\uff0c\u624d\u8ba9\u6211\u5bf9\u589e\u6839\u6709\u4e86\u66f4\u6df1\u4e00\u4e9b\u7684\u4e86\u89e3\u2026\u2026<\/p>\n<h3>\u5173\u4e8e\u8be5\u9898\u76ee<\/h3>\n<p>\u9898\u9762\uff1a\u82e5\u5173\u4e8e$x$\u7684\u65b9\u7a0b$\\dfrac{m}{x+3}-\\dfrac{1}{x^{2}-9}=2$\u6709\u589e\u6839\uff0c\u5219\u589e\u6839\u53ef\u80fd\u662f\uff08\uff09\u3002<\/p>\n<p>A. $x=3$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B. $x=-3$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0C. $x=\\pm \\sqrt{3}$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0D. $x=\\pm 3$<\/p>\n<p>\u5f53\u65f6\uff0c\u8001\u5e08\u544a\u8bc9\u6211\u4eec\u9009D\uff0c\u7406\u7531\u5f88\u7b80\u5355\uff1a\u82e5\u5206\u5f0f$\\dfrac{m}{x+3}$\u65e0\u610f\u4e49\uff0c\u5219\u589e\u6839\u53ef\u80fd\u4e3a$x=-3$\uff1b\u82e5\u5206\u5f0f$\\dfrac{1}{x^{2}-9}$\u65e0\u610f\u4e49\uff0c\u5219\u589e\u6839\u53ef\u80fd\u4e3a$x=-3,\\, 3$\u3002\u7efc\u5408\u6765\u770b\uff0c\u539f\u65b9\u7a0b\u7684\u589e\u6839\u53ef\u80fd\u4e3a$x=\\pm 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data-text=\"true\">\u4e3a0\uff0c<strong>\uff08\u6839\u4f7f\u6574\u5f0f\u65b9\u7a0b\u6210\u7acb\uff0c\u800c\u5728\u5206\u5f0f\u65b9\u7a0b\u4e2d\u5206\u6bcd\u4e3a0\uff09<\/strong>\u90a3\u4e48\u8fd9\u4e2a\u6839\u53eb\u505a\u539f\u5206\u5f0f\u65b9\u7a0b\u7684\u589e\u6839\u3002<\/span><\/p>\n<p>\u6ca1\u9519\uff0c\u4e0a\u8ff0\u5b9a\u4e49\u4e2d\u52a0\u7c97\u7684\u90e8\u5206\u6b63\u662f\u6211\u60f3\u8981\u7684\uff0c\u5b83\u8bf4\u660e\u4e86\u589e\u6839\u9700\u8981\u6ee1\u8db3\u7684\u4e24\u4e2a\u6761\u4ef6\uff1a\u662f\u539f\u5206\u5f0f\u65b9\u7a0b\u53bb\u5206\u6bcd\u540e\u5f97\u5230\u7684\u6574\u5f0f\u65b9\u7a0b\u7684\u6839\u3001\u4ee5\u53ca\u4f7f\u539f\u5206\u5f0f\u65b9\u7a0b\u5206\u6bcd\u4e3a0\u3002\u73b0\u5728\uff0c\u5728\u7ed3\u5408\u5148\u524d\u63d0\u5230\u7684\u90a3\u9053\u9898\uff0c\u67ff\u5b50\u6052\u4e0d\u6210\u7acb\u5373\u662f\u8bf4\uff1a\u5bf9\u4e8e\u4efb\u4f55$m$\uff0c$x=3$\u90fd\u4e0d\u662f\u6574\u5f0f\u65b9\u7a0b\u7684\u6839\uff0c\u6545\u4e0d\u53ef\u80fd\u662f\u589e\u6839\u3002<\/p>\n<h3>\u7b2c\u4e8c\u6b21\u4e89\u8bae\uff08\u6700\u540e\u4e00\u6b21\uff09<\/h3>\n<p>\u5176\u5b9e\u53ea\u8981\u8003\u8651\u5230\u589e\u6839\u7684\u5b9a\u4e49\uff0c\u7b54\u6848\u5c31\u4e0d\u6a21\u7cca\u4e86\uff0c\u4f46\u6211\u4e0d\u80fd\u76f4\u63a5\u8bf4\u6211\u662f\u95ee\u7684\u5ea6\u5a18\uff0c\u4e8e\u662f\u4e4e\u53c8\u82e6\u82e6\u5730\u5728\u8001\u5e08\u7684\u6559\u53c2\u4e0a\u5bfb\u627e\u76f8\u5173\u5b9a\u4e49\u2026\u2026\u8fd8\u597d\u6700\u540e\u8fd8\u771f\u8ba9\u6211\u627e\u7740\u7c7b\u4f3c\u7684\u4e86\uff08\u90a3\u4e48\u4e3a\u4ec0\u4e48\u6559\u6750\u4e0a\u7ed9\u7684\u5b9a\u4e49\u5982\u6b64\u201c\u7cbe\u7b80\u201d\u5462\uff09\uff0c\u8001\u5e08\u4e5f\u7ec8\u4e8e\u8ba4\u540c\u4e86\u6211\u7684\u89c2\u70b9\uff08\u8fd9\u6837\u8bf4\u7684\u8bdd\u611f\u89c9\u8fc7\u7a0b\u5f88\u8270\u8f9b\u4e00\u6837\uff0c\u5176\u5b9e\u53ea\u4e0d\u8fc7\u662f\u4e2a\u5b9a\u4e49\u800c\u5df2\uff08\u82e6\u7b11\uff09\uff09\u3002<\/p>\n<h3>\u8fd8\u6709\u4e00\u5904\u7279\u522b\u91cd\u8981<\/h3>\n<p>\u4e0a\u6587\u66fe\u63d0\u5230\u201c\u6574\u5f0f\u65b9\u7a0b\u7684\u6839\u201d\uff0c\u8fd9\u91cc\u7684\u6574\u5f0f\u65b9\u7a0b\u662f\u54ea\u91cc\u6765\u7684\uff1f\u662f\u539f\u5206\u5f0f\u65b9\u7a0b\u53bb\u5206\u6bcd\u540e\u5f97\u5230\u7684\u3002\u90a3\u4e48\u201c\u53bb\u5206\u6bcd\u201d\u8fd9\u4e00\u6b65\u5177\u4f53\u5982\u4f55\u64cd\u4f5c\uff1f\u5c06\u539f\u5206\u5f0f\u65b9\u7a0b\u4e58\u4e0a<strong>\u6700\u7b80\u516c\u5206\u6bcd<\/strong>\u518d\u7ea6\u5206\u5c31\u53ef\u4ee5\u5f97\u5230\u3002<\/p>\n<p>\u2014\u2014\u80fd\u4e0d\u80fd\u4e0d\u4e58<strong>\u6700\u7b80<\/strong>\u516c\u5206\u6bcd\uff0c\u800c\u662f\u76f4\u63a5\u4e58\u67d0\u4e2a\u516c\u5206\u6bcd\u5462\uff1f\u8fd9\u91cc\u6211\u4eec\u8003\u8651\u4e00\u4e2a\u7b80\u5355\u7684\u5206\u5f0f\u65b9\u7a0b$$\\frac{1}{x-1}=0.$$\u663e\u7136\u5b83\u7684\u6700\u7b80\u516c\u5206\u6bcd\u662f$x-1$\uff0c\u800c\u539f\u65b9\u7a0b\u4e58\u4e0a$x-1$\u540e\u5f97\u5230$1=0$\uff0c\u8bf4\u660e\u6574\u5f0f\u65b9\u7a0b\u65e0\u6839\uff0c\u6545\u539f\u5206\u5f0f\u65b9\u7a0b<strong>\u65e0<\/strong>\u589e\u6839\uff1b\u4f46\u662f\u6211\u4eec\u82e5\u5c06\u539f\u65b9\u7a0b\u4e58\u4e0a\u4e00\u4e2a<strong>\u975e\u6700\u7b80<\/strong>\u516c\u5206\u6bcd$(x-1)^{2}$\uff0c\u5c31\u4f1a\u5f97\u5230$x-1=0$\uff0c\u89e3\u5f97$x=1$\uff0c\u53d1\u73b0\u5b83\u662f\u539f\u5206\u5f0f\u65b9\u7a0b\u7684\u589e\u6839\uff0c\u5373\u539f\u65b9\u7a0b<strong>\u6709\u4e00\u4e2a<\/strong>\u589e\u6839$x=1$\u3002<\/p>\n<p><span class=\"\">\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u53d1\u73b0\uff1a<\/span><strong><span 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