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变量分式通分常见问题与决方法


馃専涓€銆佸垎姣嶉噷鏃㈡湁x鍙堟湁y锛岄€氬垎鏃惰鎬庝箞鍔烇紵

"鍝庡憖锛佽繖涓垎姣嶉噷鍙堟槸瀛楁瘝鍙堟槸鏁板瓧锛屽畬鍏ㄧ湅涓嶆噦鍟婏紒"鈥斺€斿垰鎺ヨЕ鍙橀噺鍒嗗紡閫氬垎鐨勬柊鎵嬶紝鍗佷釜鏈変節涓細鍙戝嚭杩欑鍝€鍤庛€傚挶浠粖澶╁氨鎷夸笁涓吀鍨嬮敊璇渚嬶紝鎶婇€氬垎杩囩▼鎷嗚В鎴?鍌荤摐寮?鎿嶄綔鎸囧崡锛?/p>


馃攳浜屻€佺鍙峰鐞嗚浜哄懡

鈥?strong>鈥嬫渚?鈥?/strong>鈥嬶細灏忔槑鎯虫妸4鈭?/span>2x3鈥?/span>鍜?span>x2鈭?/span>45鈥?/span>閫氬垎锛岀粨鏋滃啓鎴愪簡2(x鈭?/span>2)褰撳叕鍒嗘瘝銆傝繖灏卞儚鐐掕彍蹇樹簡鏀剧洂鈥斺€斿懗閬撳叏姣佷簡锛?br/> 鈥?strong>鈥嬮敊鍦ㄥ摢鈥?/strong>鈥嬶細娌℃敞鎰忓埌4鈭?/span>2x=鈭?/span>2(x鈭?/span>2)閲岀殑璐熷彿锛屾紡鎺夎礋鍙峰氨鍍忎涪浜嗛挶鍖呴噷鐨勭幇閲戯紝鏁翠釜璁$畻鍏ㄤ贡濂椼€?br/> 鈥?strong>鈥嬫纭Э鍔库€?/strong>鈥嬶細
1锔忊儯 鍏堢粰鍒嗘瘝"鍗稿"锛氭妸4鈭?/span>2x鍐欐垚鈭?/span>2(x鈭?/span>2)
2锔忊儯 鍏垎姣嶈鍖呭惈鎵€鏈?闆朵欢"锛?span>2(x+2)(x鈭?/span>2)
3锔忊儯 璋冩暣鍒嗗瓙鏃惰寰?琛ュ"锛?span>鈭?/span>2(x鈭?/span>2)3鈥?/span>瑕佸彉鎴?span>2(x+2)(x鈭?/span>2)鈭?/span>3(x+2)鈥?/span>


馃殌涓夈€佹渶绠€鍏垎姣嶆壘涓嶅

鈥?strong>鈥嬫柊鎵嬪洶鎯戔€?/strong>鈥嬶細鍒板簳鏄彇a3b2杩樻槸a2b3锛熻繖闂灏卞儚绾犵粨鍏堢┛琚滃瓙杩樻槸鍏堢┛闉嬨€?br/> 鈥?strong>鈥嬮粍閲戞硶鍒欌€?/strong>鈥嬶細
1锔忊儯 鈥?strong>鈥嬬郴鏁伴儴鍒嗏€?/strong>鈥嬶細鍙栨渶灏忓叕鍊嶆暟锛堟瘮濡?鍜?鐨勬渶灏忓叕鍊嶆暟鏄?锛?br/> 2锔忊儯 鈥?strong>鈥嬪瓧姣嶉儴鍒嗏€?/strong>鈥嬶細姣忎釜瀛楁瘝閮藉彇鏈€楂樻骞傦紙灏卞儚閫変妇瑕侀€夊緱绁ㄦ渶澶氱殑浜猴級
3锔忊儯 鈥?strong>鈥嬬壒娈婃妧宸р€?/strong>鈥嬶細閬囧埌x2鈭?/span>9杩欑寮忓瓙锛屽厛鍒嗚В鎴?span>(x+3)(x鈭?/span>3)鍐嶅姩鎵?/p>

涓句釜馃尠锛氱粰3a2b2鈥?/span>鍜?span>4ab35鈥?/span>閫氬垎
馃憠 绯绘暟鍙?锛?鍜?鐨勬渶灏忓叕鍊嶆暟锛?br/> 馃憠 a鍙?span>a2
锛宐鍙?span>b3
馃憠 鍏垎姣嶅氨鏄?span>12a2b3锛佺畝鍗曞緱灏卞儚鎷间箰楂樼Н鏈?/p>


馃З鍥涖€佸椤瑰紡鍒嗚В鎬诲崱澹?/h3>

鈥?strong>鈥嬪吀鍨嬮敊璇€?/strong>鈥嬶細鎶?span>x2鈭?/span>5x+6鐩存帴褰撴渶缁堝舰鎬侊紝鍏跺疄瀹冭兘鍒嗚В鎴?span>(x鈭?/span>2)(x鈭?/span>3)銆傝繖灏卞儚鏀跺埌蹇€掍笉鎷嗗寘瑁咃紝姘歌繙涓嶇煡閬撻噷闈㈡槸鍟ワ紒
鈥?strong>鈥嬪垎瑙e洓姝ユ硶鈥?/strong>鈥嬶細
1锔忊儯 鎵惧叡鍚屽洜瀛愶紙姣斿4鈭?/span>2x鑳芥彁涓?2鍑烘潵锛?br/> 2锔忊儯 骞虫柟宸叕寮忥紙鍍?span>x2鈭?/span>9=(x+3)(x鈭?/span>3)锛?br/> 3锔忊儯 瀹屽叏骞虫柟鍏紡锛堟瘮濡?span>x2+6x+9=(x+3)2锛?br/> 4锔忊儯 鍗佸瓧鐩镐箻娉曪紙閫傜敤浜庝簩娆′笁椤瑰紡锛?/p>

鈥?strong>鈥嬪疄鎴樻紨缁冣€?/strong>鈥嬶細缁?span>x2鈭?/span>5x+61鈥?/span>鍜?span>x鈭?/span>23鈥?/span>閫氬垎
1锔忊儯 鍒嗚Вx2鈭?/span>5x+6=(x鈭?/span>2)(x鈭?/span>3)
2锔忊儯 鍏垎姣嶉攣瀹?span>(x鈭?/span>2)(x鈭?/span>3)
3锔忊儯 绗簩涓垎寮忚涔?span>(x鈭?/span>3)锛?span>(x鈭?/span>2)(x鈭?/span>3)3(x鈭?/span>3)鈥?/span>
锛堣缁嗘楠ゅ弬鑰冪綉椤?鐨勬暀妗堣璁★級


鉂屼簲銆佸洓澶т綔姝绘搷浣滄帓琛屾

  1. 鈥?strong>鈥嬪己琛岀害鍒嗏€?/strong>鈥嬶細鎶?span>xx+y鈥?/span>绾︽垚1+y 鈫?绾﹀垎涓嶆槸鎷嗙洸鐩掞紒
  2. 鈥?strong>鈥嬫棤瑙嗚礋鍙封€?/strong>鈥嬶細鍒嗚В6鈭?/span>2x鍐欐垚2(3鈭?/span>x)杩樿寰楁病闂 鈫?璐熷彿鏄畾鏃剁偢寮桂煉?/li>
  3. 鈥?strong>鈥嬪椤瑰紡鎭愭儳鐥団€?/strong>鈥嬶細鐪嬪埌x2鈭?/span>16鐩存帴鏀惧純 鈫?鍏跺疄绛変簬(x+4)(x鈭?/span>4)鍟婏紒
  4. 鈥?strong>鈥嬮ゥ涓嶆嫨椋熲€?/strong>鈥嬶細aba+b鈥?/span>鏄庢槑宸茬粡鍚屽垎姣嶄簡杩橀€氬垎 鈫?绾睘鑴辫¥瀛愭斁灞?/li>

馃寛鐙瑙佽В锛氶€氬垎鏄暟瀛︾晫鐨?鍙樺舰閲戝垰"

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涓嬫閬囧埌鍍?span>2a2b3x鈥?/span>杩欑澶嶆潅鍒嗗紡鏃讹紝璁颁綇鍜变滑浠婂ぉ璇寸殑锛氭媶鍖呰鈫掓壘闆朵欢鈫掗槻闄烽槺銆傚氨鍍忓楠戣嚜琛岃溅锛屾憯杩囧嚑娆″氨鎺屾彙骞宠 浜嗭綖 馃毚

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