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Wir wollen auch mal den Nenner ausmultiplizieren oder \+ auf Z\344hler oder Nenner isoliert zugreifen." }{TEXT -1 0 "" }}} {SECT 1 {PARA 3 "" 0 "" {TEXT -1 15 "Vereinfachungen" }{TEXT 266 9 " s implify" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 63 "Vergleiche die verschie denen Schreibweisen und ihre Auswirkung:" }{TEXT -1 0 "" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 28 "4^0.5+3;sqrt(4)+3;4^(1/2)+3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+++++]!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\" \"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$-%%sqrtG6#\"\"%\"\"\"\"\"\" \"\"$F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "simplify auf " }{TEXT -1 59 " lezteres angewandt bringt auch unser gew\374nschtes Ergebnis: " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "simplify(4^(1/2)+3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"&" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 18 "Br\374che, Bruchterme" }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 33 "Br \374che, die nur Zahlen enthalten." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "b1:=4/7;b2:=13/5;Summe1:= b1+b2;Differenz1:=b1-b2;" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#b1G#\"\"%\"\"(" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%#b2G#\"#8\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %'Summe1G#\"$6\"\"#N" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+Differenz1G #!#r\"#N" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 22 "Br\374che mit Varia blen " }{TEXT 262 8 "simplify" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "b3:=1/x;b4:=(x-1)/x^2;Summe2:=b3+b4;Differenz:=b3-b4;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#b3G*&\"\"\"F&%\"xG!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#b4G*&,&%\"xG\"\"\"!\"\"F(\"\"\"*$)F'\"\"#F*!\"\" " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'Summe2G,&*&\"\"\"F'%\"xG!\"\"\" \"\"*&,&F(F*!\"\"F*F'*$)F(\"\"#F'F)F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*DifferenzG,&*&\"\"\"F'%\"xG!\"\"\"\"\"*&,&F(F*!\"\"F*F'*$)F(\"\" #F'F)F-" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 68 "Kein berauschendes Erg ebnis. Versuchen wir es einmal mit dem Befehl " }{TEXT 256 8 "simplify " }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "b3+b4=s implify(b3+b4);b3-b4=simplify(b3-b4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&*&\"\"\"F&%\"xG!\"\"\"\"\"*&,&F'F)!\"\"F)F&*$)F'\"\"#F&F(F)*&,&F '\"\"#F,F)F&*$)F'\"\"#F&F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&*&\" \"\"F&%\"xG!\"\"\"\"\"*&,&F'F)!\"\"F)F&*$)F'\"\"#F&F(F,*&F&F&*$)F'\"\" #F&F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 27 "So simpel kann Mathe sei n. " }}{PARA 256 "" 0 "" {TEXT -1 60 "Pr\374fe, was beim Multipliziere n und beim Dividieren passiert." }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 31 "Z\344hler und Nenner von Br\374chen " }{TEXT 263 5 "numer" } {TEXT -1 3 " " }{TEXT 264 5 "denom" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "b5:=(3*x+2)^2/(x-2)^3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#b5G*&*$),&%\"xG\"\"$\"\"#\"\"\"F+\"\"\"F-*$),&F)F,!\"#F,\"\"$ F-!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "Der Z\344hler hei\337t " }{TEXT 257 5 "numer" }{TEXT 261 4 "ator" }{TEXT 260 0 "" }{TEXT -1 19 ", der Nenner hei\337t " }{TEXT 258 5 "denom" }{TEXT 259 6 "inator " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "z:=numer(b5);n:=denom(b 5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"zG*$),&%\"xG\"\"$\"\"#\"\" \"F*\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG*$),&%\"xG\"\"\"! \"#F)\"\"$\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "expand( b5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&*$)%\"xG\"\"#\"\"\"F)*$),& F'\"\"\"!\"#F-\"\"$F)!\"\"\"\"**&F'F)*$)F,\"\"$F)F0\"#7*&F)F)*$)F,\"\" $F)F0\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(%); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,(*$)%\"xG\"\"#\"\"\"\"\"*F'\"#7 \"\"%\"\"\"F)*$),&F'F-!\"#F-\"\"$F)!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 20 "Ist folgendes klar ?" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "Ausmultiplizierter_Bruch:=expand(z)/expand(n);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%9Ausmultiplizierter_BruchG*&,(*$)%\"xG\"\"#\"\"\"\" \"*F)\"#7\"\"%\"\"\"F+,**$)F)\"\"$F+F/F'!\"'F)F-!\")F/!\"\"" }}}} {SECT 1 {PARA 4 "" 0 "" {TEXT -1 41 "Noch eine Art, Br\374che zusammen zufassen " }{TEXT 265 6 "normal" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "b6:=(2*x-1)/(x+1)-(x+1)/(x+2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#b6G,&*&,&%\"xG\"\"#!\"\"\"\"\"\"\"\",&F(F+F+F+!\"\"F +*&F-F,,&F(F+F)F+F.F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "si mplify(b6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,(*$)%\"xG\"\"#\"\"\" \"\"\"F'F*!\"$F*F)*&,&F'F*F*F*\"\"\",&F'F*F(F*\"\"\"!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "normal(b6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,(*$)%\"xG\"\"#\"\"\"\"\"\"F'F*!\"$F*F)*&,&F'F*F*F*\" \"\",&F'F*F(F*\"\"\"!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "normal(b6,expanded);" }{TEXT -1 42 "Hier steckt ein Vorteil gegen \374ber simplify" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,(*$)%\"xG\"\"# \"\"\"\"\"\"F'F*!\"$F*F),(F%F*F'\"\"$F(F*!\"\"" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 14 "normal(b3+b4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&%\"xG\"\"#!\"\"\"\"\"\"\"\"*$)F%\"\"#F)!\"\"" }}}}}}{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }