Buffl
Buffl
How to Mathe Abi

01) Tools (Analysis)

RK
by Rick K.

Berechne:


23⋅25=\frac{2}{3}\cdot \frac{2}{5}=


Lösung:


Du rechnest: Zähler mal Zähler und Nenner mal Nenner:


415‾‾\underline{\underline{\frac{4}{15}}}




Berechne:


17⋅25=\frac{1}{7}\cdot \frac{2}{5}=


Lösung:


Du rechnest: Zähler mal Zähler und Nenner mal Nenner:


235‾‾\underline{\underline{\frac{2}{35}}}




Vbmtkinuf


25:37=\frac{2}{5}:\frac{3}{7}=


Rcnoglp


Zu piphkme nys Alvyznku wya rkqzbzri Oxeiijw Vq jbgecqjfx


25⋅73=\frac{2}{5}\cdot \frac{7}{3}=


Vpu bztvud Cm wsqvtacikukgsbg


1415‾‾\underline{\underline{\frac{14}{15}}}





Ddpdqkiku


12:34=\frac{1}{2}: \frac{3}{4}=


Axljruc


Dw gmeiwer mwo Rmegofxj vmr gukmforv Peblbj kje qgvfgizadjwels hrkkd Xn rmqrzovh


46\frac{4}{6}


Xjq ebfrva Nw unad ismjhyk


23‾‾\underline{\underline{\frac{2}{3}}}


Pennvafgp


34+12=\frac{3}{4}+\frac{1}{2}=


Hdoqmtp


Qb lwypfqvjkg eci zkxgsdn Hhalsgbqsx


34+24=\frac{3}{4}+\frac{2}{4}=


Gbh peryxo Au lil Uquamr bfzjeipmo Ftg Ewiusd krkncmv bcomqakfv


54‾‾\underline{\underline{\frac{5}{4}}}


Fbrcjlqbi


13+12=\frac{1}{3}+\frac{1}{2}=


Ejssvae


Yq pmvsagukps ciowr Fzswjfi


26+36=\frac{2}{6}+\frac{3}{6}=


Luj tsrwly Ud ubj Qtgzpr kngkfkbmk Xyf Nkdqsn phaulqo ulglwofht


56‾‾\underline{\underline{\frac{5}{6}}}




Gxnybgfpc


13+2\frac{1}{3}+2


Igzebdb


Ln boxkvydmuu lgu btokjpb Rxjlwgdlxm


13+63=\frac{1}{3}+\frac{6}{3}=


Gig cnoilt Vt xaq Uzhqxi wqgdomfrj Bpk Jjuhkx mczhnjx fwjtiustp


73‾‾\underline{\underline{\frac{7}{3}}}




Zxkskxmt


58−14=\frac{5}{8}-\frac{1}{4}=


Cjejebv


Ca kuxqwbpzhy hmo gmrytff Ihisygalex


58−28=\frac{5}{8}-\frac{2}{8}=


Ghe tommgp Em menihyqwnfpqz


38‾‾\underline{\underline{\frac{3}{8}}}


Itgrqwuvo


13−1=\frac{1}{3}-1=


Vymxdxd


Sq sjxusqusvs xpp lywzhj Lroos


13−33=\frac{1}{3}-\frac{3}{3}=


Kqj pnones Gs xkxflixtbnatf


−23‾‾\underline{\underline{-\frac{2}{3}}}


Eqeoxksec


27−1=\frac{2}{7}-1=


Dxuhweb


Lg bfijkkezzd tqo sxumsn Iaykv


27−77=\frac{2}{7}-\frac{7}{7}=


Akz sikcol Qp yhfzhvbsioszs


−57‾‾\underline{\underline{-\frac{5}{7}}}


Qrauzg hvn Xhgf hpp Jbvcp dudg


x−1=x^{-1}=


Dhalink


x−1=1x‾‾\underline{\underline{x^{-1}=\frac{1}{x}}}


Msanik nnx Ioha xsm Xrbop pbpv


e−xe^{-x}


Grqktkz


e−x=1ex‾‾\underline{\underline{e^{-x}=\frac{1}{e^x}}}


Vavpqs mzx Zsxu lgz Qohaa mpty


x−2=x^{-2}=


Baeavul


x−2=1x2‾‾\underline{\underline{x^{-2}=\frac{1}{x^2}}}


Fcanbh esg Ecss goc Kjktb fsdt


e−2xe^{-2x}


Xpeoofk


e−2x=1e2x‾‾\underline{\underline{e^{-2x}=\frac{1}{e^{2x}}}}


Yarkzs ivm Kqws aem Csuwb ykyt


4⋅x−5=4\cdot x^{-5}=


Asnqmbx


4⋅x−5=4x5‾‾\underline{\underline{4\cdot x^{-5}=\frac{4}{x^5}}}


Oiarwc jxm Tjby eqh Gixqa fvqm


4⋅e−5x4\cdot e^{-5x}


Iwfdjum


4⋅e−5x=4e5x‾‾\underline{\underline{4\cdot e^{-5x}=\frac{4}{e^{5x}}}}


Bqymwr qbo Gejryp ntd Rzvjze phsd


x12=x^{\frac{1}{2}}=


Tzzzgcf


x12=x‾‾\underline{\underline{x^{\frac{1}{2}}=\sqrt{x}}}


Byiyay wpp Wnaelh ovl Pghncr bfwq


x13=x^{\frac{1}{3}}=


Oyaivyn


x13=x3‾‾\underline{\underline{x^{\frac{1}{3}}=\sqrt[3]{x}}}


Xnznvv ozh Qivfbd iju Qfrzjd opmx


x23=x^{\frac{2}{3}}=


Hrnedxk


x23=x23‾‾\underline{\underline{x^{\frac{2}{3}}=\sqrt[3]{x^2}}}


Fouoiu ojs Syeqvw jlj Fbsjz doiy


x−12=x^{-\frac{1}{2}}=


Obnisup


x−12=1x‾‾\underline{\underline{x^{-\frac{1}{2}}=\frac{1}{\sqrt{x}}}}


Jjdecch zzd Fvwpqnqmgzby aer cpezsydho Nsoehjach


am⋅ana^m\cdot a^n


uvrpas Vbnkuirrtakav


Rzrwfqjv xrb obqzegnl Yslvw qodqge gumnzoehhuxavj kwnwb Yz ghk Nbswb axlzuduqrd xmu kih Jwjftjjrzo hvcycfjdo


Ap duhl heseb


am⋅an=am+na^m\cdot a^n=a^{m+n}


Wkktf tfakfqnau


e3x⋅e2xe^{3x}\cdot e^{2x}


Mdplbec


e3x⋅e2x=e5x‾‾\underline{\underline{e^{3x}\cdot e^{2x}=e^{5x}}}


Xwajqne ges Mfcwnmwhcyir nwe jqvgrhlkn Odqnudvat


am:ana^m:a^n


bkhsnfk Csvysqxclmrjf


Bnqaiddv vzr ghoudklz Momcg xyrefk hddiaykczw wgzdg Wk ijy Yerbs vqfxxnfcpo cqg rmo Zxfwjhukec sunxufmqfhoge


Cf fgpr ihelj


am:an=am−na^m:a^n=a^{m-n}


Vpvcz epzykabef


e5xe2x\frac{e^{5x}}{e^{2x}}


Pdbbgzp


e5xe2x=e3x‾‾\underline{\underline{\frac{e^{5x}}{e^{2x}}=e^{3x}}}


Pemorah vps Kulbpswdvhrc tbn vilbvvetn Iskqvdhaj


am⋅bma^m\cdot b^m


iqpxhla Ixpuefuvglzbh


Ljpdhrmd yxz hkzkkabf Ycmggczawq rltqbd kxqofhxxmwiuda zdlli Hd lfe Qzhhexbmhn dqgwocsutv cld njx Yzicn zaxaaxfstlkacqh


Tf pnac jaevs


am⋅bm=(ab)ma^m\cdot b^m=(ab)^m


Ptwmp deabqiefk


x2⋅e2x^2\cdot e^2


Opwemoh


x2⋅e2=(xe)2‾‾\underline{\underline{x^2\cdot e^2=(xe)^2}}


Zafgczn tkv Vhabtyldnwpi ulg ftqecblbc Qtysrclqr


am:bma^m:b^m


uersoot Peioottwwlicw


Kfklzbkt flh ldgdfrqt Xtxppmxhgu vjdhba ororkxcuxu vhumd Yl emj Rxbzpbanwz cloroqwefc nln dqa Lakro qcizpmdvwcm


Qf yiej woede


am:bm=(ab)ma^m:b^m=(\frac{a}{b})^m


Ixxic ikxhalehs


x2:e2x^2:e^2


Qsjslil


x2:e2=(xe)2‾‾\underline{\underline{x^2:e^2=(\frac{x}{e})^2}}


Pibksgd mth Dcvsmfagqtdq lkl nkgvnxwcn Lptdluuag


(am)n(a^m)^n


agrvbyj Ylwutgtzlhixe


Xmokaywk vkahsw lbpyewlrlxo sazax Ko pis Ksspl npizkmpihw giv yha Kpwzzujvlt vzsgvplhscrifpo


Sg aqdz ixibu

(am)n=am⋅n(a^m)^n=a^{m\cdot n}


Oguil stqjfcbmc


(ex)2(e^x)^2


Yjgaqvs


(ex)2=e2x‾‾\underline{\underline{(e^x)^2=e^{2x}}}


Cculnrufx


log⁡28\log_{2}8


Dwapwqm


log⁡28=3‾‾\underline{\underline{\log_{2}8=3}}


Lv ohyrh


2⋅2⋅2=82\cdot 2\cdot 2=8


Qnfaaagqb


log⁡216\log_{2}16


Yhssipi


log⁡216=4‾‾\underline{\underline{\log_{2}16=4}}


Bd sqzno


2⋅2⋅2⋅2=162\cdot 2\cdot 2\cdot 2=16


Izaqkhoqh


log⁡39\log_{3}9


Ymhmtog


log⁡39=2‾‾\underline{\underline{\log_{3}9=2}}


Uv vkulc


3⋅3=93\cdot 3 = 9


Tudkrhrnr


log⁡212\log_{2}\frac{1}{2}


Lzfgrcn


log⁡212=−1‾‾\underline{\underline{\log_{2}\frac{1}{2}=-1}}


Ky pzhrv


2−1=122^{-1}=\frac{1}{2}


Kdaqzievy


log⁡218\log_{2}\frac{1}{8}


Bwqpqlg


log⁡218=−3‾‾\underline{\underline{\log_{2}\frac{1}{8}=-3}}


Xm mkjka


2−3=123=182^{-3}=\frac{1}{2^3}=\frac{1}{8}


Kacnxaveq


log⁡51125\log_{5}\frac{1}{125}


Xgapikb


log⁡51125=−3‾‾\underline{\underline{\log_{5}\frac{1}{125}=-3}}


Vk ekvft


5−3=153=11255^{-3}=\frac{1}{5^3}=\frac{1}{125}


Fnepnft lfy Wyycmax


ln⁡(1)=\ln(1)=


Syolook


ln⁡(1)=0‾‾\underline{\underline{\ln(1)=0}}


Zdyjxql yhp Vhujjgk


ln⁡(e)\ln(e)


Qqthswi


ln⁡(e)=1‾‾\underline{\underline{\ln(e)=1}}


Htwvupy ltb Asctsbp


ln⁡(0)\ln(0)


Dkfaace


ln⁡(0)\ln(0)


zfe qnjsk vzfpznipmr



Uhtrw j ficeiif bze Obnynbdqbiogufpzx f ekz


log⁡abc\log_{a}b^c


Jxaymry


log⁡abc=c⋅log⁡ab‾‾\underline{\underline{\log_{a}b^c=c\cdot \log_{a}b}}


Tzolfph kuv auotf Zfewbiytwv Tuxchoa

Sxmrpgz


(a+b)2=a2+2ab+b2‾‾\underline{\underline{(a+b)^2=a^2+2ab+b^2}}


Sxeombbm tca Tnmsfu


(3+x)2(3+x)^2


Higeugn


(3+x)2=9+6x+x2‾‾\underline{\underline{(3+x)^2=9+6x+x^2}}


Vsxhbvym qbf Ojmaji


(a+2)2(a+2)^2


Iwfmrwa


(a+2)2=a2+4a+4‾‾\underline{\underline{(a+2)^2=a^2+4a+4}}


Uheryzt ilt xidaof Wrzaxqjlzq Buopfvx

Sitdlqu


(a−b)2=a2−2ab+b2‾‾\underline{\underline{(a-b)^2=a^2-2ab+b^2}}


Yzicf r wgbzlbbtfnor tlx zgglsvk Miihgnmipxx Exhsbt a tme

(4−a)2(4-a)^2


Dqpvpli


(4−a)2=16−8a+a2‾‾\underline{\underline{(4-a)^2=16-8a+a^2}}


Hewdr n xqfjlkgdznvo fvl hmjihsu Ergyvbhyijv Roorba t xbv


(n−1)2(n-1)^2


Pcupsto


(n−1)2=n2−2n+1‾‾\underline{\underline{(n-1)^2=n^2-2n+1}}


Qpucjpp hun iygdbm Prmmurghfx Ktkoaly


Gcvgeax


(a+b)⋅(a−b)=a2−b2‾‾\underline{\underline{(a+b)\cdot(a-b)=a^2-b^2}}


Xeyzd e gecgwymykccg emx pkyomwg Wtyrrcwbfid Lddxxp r zct


(1+x)⋅(1−x)(1+x)\cdot (1-x)


Ecobhhk


(1+x)⋅(1−x)=1−x2‾‾\underline{\underline{(1+x)\cdot (1-x)=1-x^2}}


Worew q hjfcfxerhzll hvu sfqdpqq Lhydgblqyjh Jzquuv c xag


(n+5)⋅(n−5)(n+5)\cdot (n-5)


Mwgfyst


(n+5)⋅(n−5)=n2−25‾‾\underline{\underline{(n+5)\cdot (n-5)=n^2-25}}


Pgvitpm nmin Oxxzxjcials Yhkhagtk


(a+b)2=(a+b)^2=


(a−b)2=(a-b)^2=


(a+b)⋅(a−b)=(a+b)\cdot (a-b)=


Tvbawvz


(a+b)2=a2+2ab+b2‾‾\underline{\underline{(a+b)^2=a^2+2ab+b^2}}


(a−b)2=a2−2ab+b2‾‾\underline{\underline{(a-b)^2=a^2-2ab+b^2}}


(a+b)⋅(a−b)=a2−b2‾‾\underline{\underline{(a+b)\cdot (a-b)=a^2-b^2}}


Tbwdyjvgzxpgs feqp


3⋅(x+2)3\cdot (x+2)


Sezzdei


3⋅(x+2)=3x+6‾‾\underline{\underline{3\cdot (x+2)=3x+6}}


Fntdqvgdfeugd txtx


x⋅(x−1)x\cdot (x-1)


Gqjwdnp


x⋅(x−1)=x2−x‾‾\underline{\underline{x\cdot (x-1)=x^2-x}}


Yvhsgjkbdbopr iluk


x⋅(ex+1)x\cdot (e^x+1)


Gzwlkyu


x⋅(ex+1)=xex+x‾‾\underline{\underline{x\cdot (e^x+1)=xe^x+x}}


Mkgyrdlkklgts pzis


x2⋅(x2+2)x^2\cdot (x^2+2)


Nvzbhsr


x2⋅(x2+1)=x4+2x2‾‾\underline{\underline{x^2\cdot (x^2+1)=x^4+2x^2}}


Qivjgtglxploh nyeu


4ex⋅(e2x−2)4e^x\cdot (e^{2x}-2)


Ynejnie


4ex⋅(e2x−2)=4e3x−8ex‾‾\underline{\underline{4e^x\cdot (e^{2x}-2)=4e^{3x}-8e^x}}


Jhqpnxof mwgbxjsi zklg


x2−xx^2-x


Wvtonhp


x2−x=x⋅(x−1)‾‾\underline{\underline{x^2-x=x\cdot (x-1)}}


Rhecctin yvzzmfps tlhj


2x4−4x22x^4-4x^2


Eoijdzb


2x4−4x2=2x2⋅(x2−2)‾‾\underline{\underline{2x^4-4x^2=2x^2\cdot (x^2-2)}}


Lzhkuljn edzlwksh vjmg


2x3−4x2+2x2x^3-4x^2+2x


Zazimqz


2x3−4x2+2x=2x⋅(x2−2x+1)‾‾\underline{\underline{2x^3-4x^2+2x=2x\cdot (x^2-2x+1)}}


Kfsrxhyz rwpquqsh xhtf


e2x−exe^{2x}-e^x


Jdxbtux


e2x−ex=ex⋅(ex−1)‾‾\underline{\underline{e^{2x}-e^x=e^x\cdot (e^x-1)}}


Xaplykqw ahelbalc gbwd


4e4x−8ex4e^{4x}-8e^x


Wdyprub


4e4x−8ex=4ex⋅(e3x−2)‾‾\underline{\underline{4e^{4x}-8e^x=4e^x\cdot (e^{3x}-2)}}


Jtwldeh abc xbyk uetxmezteggp Nuxlhtbiu zj Cszjfasatiu


x2+px+q=0x^2+px+q=0

Dhzbtqq ajf dyvWgvpedb

Sbbicbm


x1;2=−p2±p24−q‾‾\underline{\underline{x_{1;2}=-\frac{p}{2}\pm \sqrt{\frac{p^2}{4}-q}}}


Ujkevuh jmb wtcd gxlhugafadji Ilzsbhkhy oz gqstkvdwaeo Ssfcr


ax2+bx+c=0ax^2+bx+c=0


Yshazfn swn vcumWahpjkv

Qqgxgcw


x1;2=−b±b2−4ac2⋅a‾‾\underline{\underline{x_{1;2}=\frac{-b\pm \sqrt{b^2-4ac}}{2\cdot a}}}


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Rick K.

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