Exercise:
Löse die Gleichung zunächst unter Annahme des Normalfalls. Diskutiere dann die Sonderfälle. nprvmulticols abclist abc xp- abc cx c + abc x+p- px abc a+a+x + a-x ax + abc + b + b+x + a-x ax + abc t^+x tx - t- abc a^x+ x + abc ax abc p-x abc b+x abc b+x b- abc c+x c+ abc d-x -d^ abc p-px p^- abc s^ + sx abc t^-t-x t+ abc ax- x + b abc bx a + b + x abc a+bx a^-b^ abc a-bx a- abclist nprvmulticols

Solution:
Wir lösen zuerst unter Annahme des Normalfalls und überlegen uns dann an welchen Stellen wir potentiell durch geteilt haben. abclist abc edtxp- uf :p- x fracp- loesfracp-quad pneq loesquad p ed abc edtcx c + uf:c x fracc+c loesfracc+c quad cneq loes quad c ed abc edtx+p- px tu px-x+p- px uf -px -p + -px-x -p+ tu x-p- -p+ uf:-p- x fracp-p+ loesfracp-p+ quad pneq - loes quad p - ed abc edta+a+x + a-x ax + tu a + ax+x+a-ax ax + uf -ax-a x-ax -a tu x-a -a uf :-a x loes quad a neq frac && L R quad a frac ed abc edt + b + b+x + a-x ax + tu + b + bx + x + a - ax ax + uf -ax --b-a bx + x - ax -a -b - tu xb-a + -a-b- uf:b-a+ x frac-a-b-b-a+ tu fraca +b+a-b- loesfraca +b+a-b- quad b neq a - -a-a-- tu -a+ uf +a a uf : a frac loes quad afrac b-frac & &&L R quad ba- aneqfrac ed abc edtt^+x tx - t- uf t^x + x tx -t + uf -tx t^x - tx +x -t+ tu xt-^ -t- uf :t-^ x frac-t+t-^ loesfrac-t- quad t neq && L R quad t ed abc edta^x+ x + tu a^x + a^ x + uf -x-a^ a^-x -a^ uf :a^- x - loes- quad a notinqty- && L R quad a in qty- ed abc edtax uf :a x fraca loesfraca quad a neq loes quad a ed abc edt p-x uf:p- x fracp- loesfracp- quad pneq loes quad p ed abc edtb+x uf :b+ x loes quad bneq - &&L R quad b - ed abc edtb+x b- uf :b+ x fracb-b+ loesfracb-b+ quad bneq - - loes quad b - ed abc edtc+x c+ uf:c+ x loes quad cneq - &&LR quad c - ed abc edtd-x -d^ tu d-x +d-duf:d- x -d- loes-d-quad d neq && L R quad d ed abc edtp-px p^- uf:pp- x fracp+p loesfracp+p quad pnotinqty - loes quad p &&L R quad p ed abc edts^ + sx uf :ss+ x loes quad snotinqty- &&L R quad sinqty- ed abc edtt^-t-x t+ tu t+t-x t+ uf:t+t- x fract- loesfract- quad tnotinqty- && L R quad t - loes quad t ed abc edtax- x + b uf -x+ a-x b+ uf:a- x fracb+a- loesfracb+a- quad a neq b+ uf - - b loes quad abneq- & &&LR quad ab ed abc edtbx a + b + x uf -x b-x a+b uf:b- x fraca+bb- loesfraca+bb- quad b neq a + uf - - a loes quad b a neq - & &&LR quad b a - ed abc edta+bx a^-b^ uf:a+b x a-b loesa-b quad a neq -b -b^ -b^ &&LR quad a -b ed abc edta-bx a- uf:a-b x fraca-a-b loesfraca-a-b quad a neq b a- uf + a loesquad a b neq & &&L R quad a bfrac ed abclist