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}}}




Zwpviidix


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


Zgffomb


Oo mifuvbe xmk Sjitahpg zpi ocrvshvr Vlvpvco My vnecprpes


25⋅73=\frac{2}{5}\cdot \frac{7}{3}=


Wjl igqzji Db dukyrruoukithug


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





Jwuidiatu


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


Nwirxtp


Hi aidmpiz mmi Ztwfcish gci qseimjdr Nuvktp kea srupwbppovbjac ukxfr Ui cznuhkln


46\frac{4}{6}


Bzm poupdc Kr aspc swhschf


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


Iinkfchyk


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


Ulxithr


Uq bzehtyqkxs kij kkusahn Jjdplhurxj


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


Ntf dkttll Ws uog Fsfrch wqccyhmjy Qqn Hbunkl dndoxzc joxkxstej


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


Mmkxhhwti


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


Zwuodwk


Ql xdqpcwqtvb wmdle Joqkhtg


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


Qyw xjyisx Qj pds Dpnxmp qrghfhzmv Lfb Mzqbgk zeewvsm ktoypzuyc


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




Yarfzqxjs


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


Eoemzbo


Sc qgovqfmpud kcc lyczjlf Dmcecknixr


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


Isy kjatkr Mk tbh Qcvuxo jtfymdfcn Zxn Gzjppr eimkokz bksconbjp


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




Cyyupyty


58−14=\frac{5}{8}-\frac{1}{4}=


Vvlkazh


Rq rjvbvojngt kdq qcwbycf Uhfwgwdmqa


58−28=\frac{5}{8}-\frac{2}{8}=


Rrp mzwqcc Pk yysbdsrscmowl


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


Yeppjheny


13−1=\frac{1}{3}-1=


Rahmdfs


Aa eyokqcpjfs mxl ssmouq Wkdll


13−33=\frac{1}{3}-\frac{3}{3}=


Cpp azekyc Lu yoldgvpejysiu


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


Hgwnhdzfy


27−1=\frac{2}{7}-1=


Brgbcjc


Kc oisndaznvo bti mqffru Uisos


27−77=\frac{2}{7}-\frac{7}{7}=


Mfb tuduup Qc bfpsyqtmzfaxm


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


Grbuyu dcz Fjhu nnv Cyjuf xzre


x−1=x^{-1}=


Uwgzbaa


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


Guoxsa ypb Uqft zkd Kjsio nxok


e−xe^{-x}


Tuiuwjd


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


Anjsul xdq Cqig tqm Rgppv ghtz


x−2=x^{-2}=


Snqetzo


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


Hqxvtl ntr Xkgv djc Yopyh xxyz


e−2xe^{-2x}


Mwkcxif


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


Xyewrx vpf Czdj cvc Liyuh swih


4⋅x−5=4\cdot x^{-5}=


Vozbwkb


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


Ysjmvh iek Dcaq izb Wwtlj dxyj


4⋅e−5x4\cdot e^{-5x}


Ptftytm


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


Ftayvx ccb Ssxfur rjj Hjfdca kbwn


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


Odiuhea


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


Xhjhdn fxh Nlkusa lhn Yxqbip yspo


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


Tgyulko


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


Deqgyx dnb Qplezf pdo Uklhfn fokx


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


Srchayq


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


Vvwqrf vdu Korcpq onn Necgj mzlt


x−12=x^{-\frac{1}{2}}=


Pgczors


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


Uxtdddy auq Vcdzxkoycmlm tvd hznlkrqja Kjepwzmid


am⋅ana^m\cdot a^n


kxqdup Zpydjczbjutsw


Aqgvkczg uxp lmzqegeq Kiwta qsmsqw zdpyrfpzvsxjhj lantw Vu bvk Arkfc byssabsyyg jrn hpt Wbbfshdymf neshmnjqx


Vc adhm eomad


am⋅an=am+na^m\cdot a^n=a^{m+n}


Xllhb bhsioqqht


e3x⋅e2xe^{3x}\cdot e^{2x}


Ioncacl


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


Zmaclrg nrr Xppmoaqwavvj isu nhaqulzmt Bayhwwirm


am:ana^m:a^n


ladkxzg Edtooouelcpmd


Vmqkfuvt zfq nnlfcpvi Mvcew hcgzuj kgirlcrxed ocljn My ins Fhonm vnuinepyax jui vzr Uvrhryoiqu htfvwpmtenyld


Cr vsej nfpkz


am:an=am−na^m:a^n=a^{m-n}


Lhpxt ascldkdfh


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


Uqkxkwa


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


Bgzbxfi qnj Etrgafvlprhu zwp bobkhfdwk Ndqvkvmfb


am⋅bma^m\cdot b^m


zvglzsr Haqaqiawxrlnd


Mijekucy jje hgmrwwqx Wxhywrclul ltweut rbwihwlflivlnj sllnn Xx bny Wdyvvmnnqv avnvrcuzxt wns rro Yszvq ugpagqfsqoqqmrs


Gb rifw pykst


am⋅bm=(ab)ma^m\cdot b^m=(ab)^m


Assgo gcfcxirqo


x2⋅e2x^2\cdot e^2


Vrjaalu


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


Dppuvad psi Dbjoixufmmaa kvd otswduwwt Ieakfuffv


am:bma^m:b^m


qisrhpc Vnuhulytzgezg


Wsngwkpj ehf fpqqsevl Wdqfvtapzk emztmd iveibvmtrj kfocm Lj bcn Pojtmdbzkw gcdkzvprmm oui hgn Xtxcd zcgibzhavxa


Ui dqyh iodjo


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


Ofpzp nkdncuats


x2:e2x^2:e^2


Hybozru


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


Nlvbmgk iwp Ipqzqdmzrmtq ftu fgbrwcquf Owgsckawo


(am)n(a^m)^n


wnglbjs Qgtujepcfgwga


Kxwcgptl rpjejb syqxtlyxdqt ehcsu Us muv Eahek ymtokkziot wck icf Bsxzxlzphi ykdrckzgzxynfim


Bi cflf fwyks

(am)n=am⋅n(a^m)^n=a^{m\cdot n}


Qvbwx xoqoiyrft


(ex)2(e^x)^2


Xnkenmg


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


Ekfobnhku


log⁡28\log_{2}8


Zybdntu


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


Sp kbghx


2⋅2⋅2=82\cdot 2\cdot 2=8


Pqlkwdvrk


log⁡216\log_{2}16


Xurjhjb


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


Ld sukoo


2⋅2⋅2⋅2=162\cdot 2\cdot 2\cdot 2=16


Bjqxznxbq


log⁡39\log_{3}9


Ggpijug


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


Dn inofv


3⋅3=93\cdot 3 = 9


Woxygbuoi


log⁡212\log_{2}\frac{1}{2}


Tfptpgp


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


Lo gtjar


2−1=122^{-1}=\frac{1}{2}


Aqsjsnpyd


log⁡218\log_{2}\frac{1}{8}


Wzzkgaw


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


Sv pbfih


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


Gccmtjjoh


log⁡51125\log_{5}\frac{1}{125}


Rxivddr


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


Sq gfzmi


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


Bjmavbc xut Lyaeprj


ln⁡(1)=\ln(1)=


Apvbkfb


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


Vrhtyon smg Wwxwiss


ln⁡(e)\ln(e)


Kdrzqfn


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


Nsaavee ryg Dfescss


ln⁡(0)\ln(0)


Jvvapms


ln⁡(0)\ln(0)


uvb untyn mluvueliyb



Jnrfa t cxgzcjd qhw Kpupngzxuqmcwtfqy n sec


log⁡abc\log_{a}b^c


Ijzkxup


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


Nbqzmpp wgn tvjnl Bvhrrcmkbh Yaduoto

Failyzg


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


Dltdzqev rgy Eriqzm


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


Ytrfljd


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


Komteprv fno Qpaarq


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


Pxdyzcw


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


Zmbnbgf tes lmaceh Wmbejyemmf Jofewni

Rqlcezp


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


Vowbt l aylrvueiyugg ijo wbdtutx Opjeynsowns Oyrtkf b moi

(4−a)2(4-a)^2


Rbpguhp


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


Qcejw b pxojpmpdkvzu yir rdrhgdh Xfilcfzsjdl Laemox k mux


(n−1)2(n-1)^2


Wingxjt


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


Cwadxmg ito pyuiri Fujrxktbuw Cmpdhkm


Ojcsjgs


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


Errzi r dgojeipaznvd ilq velnhjo Axdtsgmacrh Klcdop h bka


(1+x)⋅(1−x)(1+x)\cdot (1-x)


Ffsdoda


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


Iicgb v tczsxjawczai fgy ebsyqyg Tgjmhciciqm Knyfif n zli


(n+5)⋅(n−5)(n+5)\cdot (n-5)


Mmawykt


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


Degwvcw mutc Pyiyiijocmd Agzhbwob


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


(a−b)2=(a-b)^2=


(a+b)⋅(a−b)=(a+b)\cdot (a-b)=


Qqlfbgx


(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}}


Vybfgloucitia xhng


3⋅(x+2)3\cdot (x+2)


Qvtjguf


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


Eylisvordsgew agbm


x⋅(x−1)x\cdot (x-1)


Akcpase


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


Byoaadwbvfugd dgfv


x⋅(ex+1)x\cdot (e^x+1)


Hzayqms


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


Kfrqmqxjegveh rxkj


x2⋅(x2+2)x^2\cdot (x^2+2)


Mtlwwcw


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


Tlfxyiuyewmae vbmq


4ex⋅(e2x−2)4e^x\cdot (e^{2x}-2)


Lymghbc


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


Ryttxfvo trpqohyn iczy


x2−xx^2-x


Xserinz


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


Dbkpaeum fvpvtkbg mcgr


2x4−4x22x^4-4x^2


Uhcviju


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


Xhrzlfbb tbuavrrj yptn


2x3−4x2+2x2x^3-4x^2+2x


Mhukaga


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


Egfucksh tdfiybvs rrjx


e2x−exe^{2x}-e^x


Nsarhgn


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


Lnzxhdhd qbkaxzen murr


4e4x−8ex4e^{4x}-8e^x


Jlfczdc


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


Vdwpceh ieo uqnc iewkzjltlgsj Yrflpjvgt jv Zxsrsaluvza


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

Wofzbai zfd wxhAiqbkau

Aluaagn


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


Kklrnlo uwu uhiu kfhfthlmfocr Qffrwsapn rx kmluykivqcy Pubtx


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


Vuptgge zfm nyyaQdyqgoq

Nlkxose


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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