【答案】
分析:解決本題的關(guān)鍵是根據(jù)abc=1的條件,將所求的代數(shù)式通分,然后進(jìn)行分式的加減運(yùn)算.
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=
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,將abc=1代入后,可得:
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=
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;
同理,可知:
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=
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=
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;由此,三個(gè)分式的分母都化成了ab+a+1,然后根據(jù)分式的加減法運(yùn)算規(guī)則進(jìn)行計(jì)算即可.
解答:解:∵abc=1,
∴原式=
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=
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+
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+
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=
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=1.
點(diǎn)評(píng):分式中的一些特殊求值題并非是一味的化簡(jiǎn),代入,求值.許多問(wèn)題還需運(yùn)用到常見(jiàn)的數(shù)學(xué)思想,如化歸思想(即轉(zhuǎn)化)、整體思想等,了解這些數(shù)學(xué)解題思想對(duì)于解題技巧的豐富與提高有一定幫助.就本節(jié)內(nèi)容而言,分式求值題中比較多的題型主要有三種:轉(zhuǎn)化已知條件后整體代入求值;轉(zhuǎn)化所求問(wèn)題后將條件整體代入求值;既要轉(zhuǎn)化條件,也要轉(zhuǎn)化問(wèn)題,然后再代入求值.