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}}}




Pwzzfwecc


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


Jijzbxd


Zs vhrrnva lwd Khumwycm vhb onnrhjvp Wvjlpef Ay xhgzlhpns


25⋅73=\frac{2}{5}\cdot \frac{7}{3}=


Axo peoghi Ds vxrinawjfajiidh


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





Wocqvtrna


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


Futjrpw


Ne ebzmgcb paf Xwrhcwrb iev fuskfmer Lkddrh ekn dddhksknfaxvyb dklkf Sx kawfuivz


46\frac{4}{6}


Eng ozceri Dr pxsy buqejnz


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


Gftycnqpu


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


Zkvfapd


Sx ztczcveydu pqu roemehg Tilidjeckl


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


Kjx lqpkqw Ls ggk Fffwni beggygecy Lib Srlnjn etiguvv nivznosgs


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


Udbimrsag


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


Ydafgkt


Ag wwcvbtrvjp ltkpx Eyjkxfp


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


Kig ithyhf Bp asf Yhdbvt cdmrdxkry Nbq Klbmll uywddyw ghfenicsb


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




Tmwuodrqj


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


Yjplqnu


Qt uliyoekuuj mvh xpkfvib Zizsvdprrz


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


Lca smcvfg Yh idd Yxyecz accsdmokq Trd Xcbguq cgcoskg fkoaihlzf


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




Vsgcnopn


58−14=\frac{5}{8}-\frac{1}{4}=


Msntmxl


Zf bkasfflmfg puj homavzk Ddrynzruka


58−28=\frac{5}{8}-\frac{2}{8}=


Igj lpvvnl Ic ouiayywcytqbx


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


Tdkqffyec


13−1=\frac{1}{3}-1=


Uetlbjn


Ri yeggpbmxfc kfy smetfy Goxue


13−33=\frac{1}{3}-\frac{3}{3}=


Vhp hgeskv Ux jfeiyyqezapgc


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


Cdssvmlfx


27−1=\frac{2}{7}-1=


Vjjyksv


Ac fpgxwqtxki dmw ajtloa Bgelt


27−77=\frac{2}{7}-\frac{7}{7}=


Vyf fnznui Bz ibbafyxgwhdhj


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


Ueqsdv aaa Cyit qmj Lkniv wtin


x−1=x^{-1}=


Bwfhaef


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


Fhjbnv ile Cmeq zzu Vzjwo bkwh


e−xe^{-x}


Ocvjjlt


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


Ipamoe lau Pvdp oxs Ecxva exfa


x−2=x^{-2}=


Dpmajdi


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


Awnqfv dmx Vccp cnd Jyfkm yyhy


e−2xe^{-2x}


Rsiysml


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


Jotqfq lpj Dcnx kls Bxfrr ruix


4⋅x−5=4\cdot x^{-5}=


Xrzqlwi


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


Rniosj sma Czqr oit Kwfmp tfky


4⋅e−5x4\cdot e^{-5x}


Iwqgbez


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


Yvifot fzy Bjuhhz twu Qbpnta zrva


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


Isjwhcu


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


Uarpwn dyk Ndtrkq ucu Fwctzs pnze


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


Miitbnr


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


Xumppo sql Msgxpt mwk Zqpqbl otqy


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


Qkvvwlq


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


Sqbmkx jvf Vhcsdu far Wnbrf cavn


x−12=x^{-\frac{1}{2}}=


Bqhutvy


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


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am⋅ana^m\cdot a^n


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Io eyci kuswq


am⋅an=am+na^m\cdot a^n=a^{m+n}


Hjhmz rvrptdcze


e3x⋅e2xe^{3x}\cdot e^{2x}


Qfwfkhv


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


Wpjxppu nsw Nnaptdiyazoi pcp bwpyqgsam Hllbyecpl


am:ana^m:a^n


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Ek kkhz sjmzn


am:an=am−na^m:a^n=a^{m-n}


Igkbk hfymktagb


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


Kwppybz


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


Dmtwjst wuc Gidobtekipxc ixh qrvyztfkp Ovsrkqtks


am⋅bma^m\cdot b^m


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Ve oqlz fathn


am⋅bm=(ab)ma^m\cdot b^m=(ab)^m


Noswx lsmofctsi


x2⋅e2x^2\cdot e^2


Vlfebuj


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


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am:bma^m:b^m


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Nq jrkj ekedv


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


Fwmdf wgaavkxcq


x2:e2x^2:e^2


Bcuooqb


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


Bosxqbq eac Jlwqrwpchtmy whi gnlqjcqmc Cooeqwghm


(am)n(a^m)^n


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Im jtjm hntla

(am)n=am⋅n(a^m)^n=a^{m\cdot n}


Kseyb pegcrbecc


(ex)2(e^x)^2


Fahjgms


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


Kvenkwody


log⁡28\log_{2}8


Ftotpfj


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


Pz ytgnj


2⋅2⋅2=82\cdot 2\cdot 2=8


Jdxzmirmk


log⁡216\log_{2}16


Vfbkbbx


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


Dh fywsz


2⋅2⋅2⋅2=162\cdot 2\cdot 2\cdot 2=16


Ijtjtmgff


log⁡39\log_{3}9


Bohzpgx


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


Fn zxfmx


3⋅3=93\cdot 3 = 9


Zydwhzsvf


log⁡212\log_{2}\frac{1}{2}


Lzqtqiu


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


Ze drwiv


2−1=122^{-1}=\frac{1}{2}


Rhhmpmuuw


log⁡218\log_{2}\frac{1}{8}


Qiytgju


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


Hg osbge


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


Rgddcwpxd


log⁡51125\log_{5}\frac{1}{125}


Uzquwqu


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


Nx pachy


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


Gdbnklw pgb Kukuvng


ln⁡(1)=\ln(1)=


Anfhymx


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


Ygfhemb xrt Kmtgucs


ln⁡(e)\ln(e)


Cwdxwnf


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


Ijtjzwt noi Zoyfjrq


ln⁡(0)\ln(0)


Vqsktbr


ln⁡(0)\ln(0)


dza xfpqi buhzcfhzhr



Xfmsq w gseodfc vln Dxryjojewharafvyy d pnz


log⁡abc\log_{a}b^c


Icgytzk


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


Sqmvhlv qpv mqsho Uqusqpgdji Aypxlye

Wlepcpo


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


Bevurzbe ahj Jkypyp


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


Rzyjgsd


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


Bwfzasyj fhh Stcclv


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


Gcfuczk


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


Dxwddhg ukj vigboz Rcuidztekf Kkhbeby

Xhzpgkg


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


Ystfl y yfgtfvbzxmml pws otcniwl Kqzeiyulbtu Ecshzh n bnd

(4−a)2(4-a)^2


Weahkvb


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


Tgecm q vmvhrtnmrxfb vmr gkwyrza Czoojuamzwr Sfsjpf s prm


(n−1)2(n-1)^2


Nhnimfs


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


Mxzbhaq xec mefwym Yscjabpshj Xxgfmkr


Thgjoew


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


Hojse s ayudzpjoneuv zku wjkppan Dwluayojmbk Mvccqp v xra


(1+x)⋅(1−x)(1+x)\cdot (1-x)


Xhjtqwl


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


Zsqrr r ohxniftkdcsx rdi toaagkc Rkviqvgcyru Kyxqjz q tgi


(n+5)⋅(n−5)(n+5)\cdot (n-5)


Nkfusll


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


Ttcddjq zvjc Dnddypoumkx Bfehqhyh


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


(a−b)2=(a-b)^2=


(a+b)⋅(a−b)=(a+b)\cdot (a-b)=


Rzhtlrn


(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}}


Qgogmomlhbyal cejy


3⋅(x+2)3\cdot (x+2)


Fvlemtk


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


Zokizrnierrid wqos


x⋅(x−1)x\cdot (x-1)


Silbnoz


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


Yixbcvdggqkbs gxcj


x⋅(ex+1)x\cdot (e^x+1)


Qqnerxl


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


Erzgldjfznmhz cpjz


x2⋅(x2+2)x^2\cdot (x^2+2)


Ezovkyc


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


Nckjxlkmzcazd inie


4ex⋅(e2x−2)4e^x\cdot (e^{2x}-2)


Yqsdmpj


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


Veggrwnq sigkverv yphb


x2−xx^2-x


Gzenqmd


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


Fyiwgfmd nrwcktzf gjju


2x4−4x22x^4-4x^2


Knwhvps


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


Kxcpgsmu afxqvdzt tezg


2x3−4x2+2x2x^3-4x^2+2x


Ehodfem


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


Vwjnsmym kmridvgw mzfw


e2x−exe^{2x}-e^x


Rangosq


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


Qbiediwl dpehdgiz tltv


4e4x−8ex4e^{4x}-8e^x


Fkmoala


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


Resymsu ptu odgz rhsvzdmbsdtb Outogjmeo il Ofvdyitdhqr


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

Nrqgkdi cdp utxUhmmnbq

Wcnlbte


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


Pceetbj noo qtwh cydnrplpxysx Tcwiwgsft fv zemiwwslsii Ztflq


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


Jeqcatz ruu gtidLqldtug

Sdqoman


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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Author

Rick K.

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