培优专题四-五 分式的运算技巧 分式化简求值的几种常见类型-【练测考】2023-2024学年八年级上册数学（鲁教版五四制）

两年后!华罗庚被破格提升为助教!继而升为讲师 ! 后来!熊庆来又送他去英国剑桥大学深造 !#0%4 年!华罗庚回国!任西南联大教授!当时他才 $4 岁 ! #待续$ ()*+F-#".GHIJ !!!!!!!!!!!!!!!! /0$% Þßठ!! 若" $ ) # % ) , " !则$"#*%#,*"," " $ * # $ *, $ ) !!!! ! "! 已知 $%& - / !并且$*% & ) %*& $ ) &*$ % ) ) !则 直线 # ) ) "* ) 一定通过第 !!!! 象限 ! #! 若"*#(, , ) "( # *, # ) ("* # *, " !求 " * # #" # *, #" ,*" # " # , 的值 ! /0&% Ú#-J $! !母积子差"计算$$(% $% * %(& %& * &($ &$ ! %! !母积子和"计算$$*% $% ( %*& %& ( &*$ &$ ! &! !直接裂项"计算$ # $ " $*# # * # " $*# #" $*$ # * # " $*$ #" $*% # * + * # " $*#0 #" $*$/ # ! /0'% áJâ> 基本模型$ "* # " # " $ )" $ * # " $ *$ ! "( # " # " $ ) " $ * # " $ ($! '! 已知 ' $ (.'(#)/ !计算 $' $ (.'* # ' $ 的值 ! (! 已知 " " $ (%"*# )# !求 " $ " " (0" $ *# 的值 ! )! 若正数 $ ! % ! & 满足 $%&)# ! $* # % )% ! %* # & ) #1 !则 &* # $ ) !!!! ! /0(% “V+ !*! 一般情况下!一个分式通过适当的变形!可 以化为整式与分式的和的形式! 例如$ ! "*# "(# ) " (# # *$ "(# ) "(# "(# * $ "(# )#* $ "(# & " " $ "($ ) " $ ("*" "($ ) " *$ #" ($ # *" "($ )"*$* " "($ ! " # #试将分式"(# "*# 化为一个整式与一个分 式的和的形式& " $ #如果分式$" $ (# "(# 的值为整数!求 " 的整 数值 " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " ! #% BTS:#"(#"px 华罗庚后来成为世界著名的数学家!在很多领域都做出了卓越的贡献 ! 他的名字被列为当今八十八 个数学伟人之一 ! ()*+K-#"LMNO.PQRSTU !!!!!!!!!!!!!!!! /0$% eK#"ZãäQRMN !! !资阳中考"化简求值$ " $ " $ (# # (# : # " $ *" ! 其中 ")$! "! !菏泽中考改编"先化简!再求值$ # "( # % $ # "* # # (# : # # $ (" $ !其中 ") # * $/$#! #! 先化简!再求值$ "( $" # ( # $ " # " : " $ ( # $ " $ *" # ! 其中 ")槡$!#)槡$(#! /0&% eK#"ZåRQæMN $! !常德中考"先化简!再选一个合适的数代入 求值$ "*#( 1"(0 " # " : " $ (0 " ! %! !常德中考"先化简!再选一个合适的数代入 求值$"(# " $ *" ( "(% " $ # (# : $" $ *"*# " $ (" " # (# ! /0'% eK#"Z)•QRMN &! !烟台中考"先化简!再求值$ #* " $ *$ " " # ($ : "*# " $ (""*" !其中 " 满足 " $ ($"(.)/ " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " ! #& 789:;<=>?:@A 分式方程的历史及现代应用 ! 古埃及人利用许多数学形式来解决实际问题!而分式方程就是其中之 一 ! 古埃及文明拥有丰富的有关建筑+数学和艺术的古代文献 ! #待续$ '! 先化简!再求值$ $ $ (" $ $ ("$*" ( # $( " # $ : $ $ $ ($$ ! 其中 $ 满足 $ $ *%$($)/!