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\frac{9x\left(x+1\right)}{8}
Víkka
\frac{9x^{2}+9x}{8}
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Afritað á klemmuspjald
\frac{\frac{\left(x-2\right)\left(x-2\right)}{\left(x-2\right)\left(x+1\right)}+\frac{\left(5-x\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
Til að leggja saman eða draga saman segðir skaltu stækka þær til að nefnararnir verði eins. Minnsta sameiginlega margfeldi x+1 og x-2 er \left(x-2\right)\left(x+1\right). Margfaldaðu \frac{x-2}{x+1} sinnum \frac{x-2}{x-2}. Margfaldaðu \frac{5-x}{x-2} sinnum \frac{x+1}{x+1}.
\frac{\frac{\left(x-2\right)\left(x-2\right)+\left(5-x\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
Þar sem \frac{\left(x-2\right)\left(x-2\right)}{\left(x-2\right)\left(x+1\right)} og \frac{\left(5-x\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)} eru með sama nefnara skaltu leggja saman með því að leggja saman teljarana.
\frac{\frac{x^{2}-2x-2x+4+5x+5-x^{2}-x}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
Margfaldaðu í \left(x-2\right)\left(x-2\right)+\left(5-x\right)\left(x+1\right).
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
Sameinaðu svipaða liði í x^{2}-2x-2x+4+5x+5-x^{2}-x.
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{\left(x-2\right)\left(x+1\right)}-\frac{1}{\left(x+1\right)\left(x+2\right)}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
Stuðull x^{2}-x-2. Stuðull x^{2}+3x+2.
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{x+2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}-\frac{x-2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
Til að leggja saman eða draga saman segðir skaltu stækka þær til að nefnararnir verði eins. Minnsta sameiginlega margfeldi \left(x-2\right)\left(x+1\right) og \left(x+1\right)\left(x+2\right) er \left(x-2\right)\left(x+1\right)\left(x+2\right). Margfaldaðu \frac{1}{\left(x-2\right)\left(x+1\right)} sinnum \frac{x+2}{x+2}. Margfaldaðu \frac{1}{\left(x+1\right)\left(x+2\right)} sinnum \frac{x-2}{x-2}.
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{x+2-\left(x-2\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
Þar sem \frac{x+2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)} og \frac{x-2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)} eru með sama nefnara skaltu draga frá með því að nota frádrátt á teljarana.
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{x+2-x+2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
Margfaldaðu í x+2-\left(x-2\right).
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
Sameinaðu svipaða liði í x+2-x+2.
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x\left(x+1\right)}\right)}
Stuðull x^{2}+x.
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{\left(x+1\right)\left(x+1\right)}{x\left(x+1\right)}+\frac{3-x^{2}}{x\left(x+1\right)}\right)}
Til að leggja saman eða draga saman segðir skaltu stækka þær til að nefnararnir verði eins. Minnsta sameiginlega margfeldi x og x\left(x+1\right) er x\left(x+1\right). Margfaldaðu \frac{x+1}{x} sinnum \frac{x+1}{x+1}.
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\times \frac{\left(x+1\right)\left(x+1\right)+3-x^{2}}{x\left(x+1\right)}}
Þar sem \frac{\left(x+1\right)\left(x+1\right)}{x\left(x+1\right)} og \frac{3-x^{2}}{x\left(x+1\right)} eru með sama nefnara skaltu leggja saman með því að leggja saman teljarana.
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\times \frac{x^{2}+x+1+x+3-x^{2}}{x\left(x+1\right)}}
Margfaldaðu í \left(x+1\right)\left(x+1\right)+3-x^{2}.
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\times \frac{2x+4}{x\left(x+1\right)}}
Sameinaðu svipaða liði í x^{2}+x+1+x+3-x^{2}.
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4\left(2x+4\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)}}
Margfaldaðu \frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)} sinnum \frac{2x+4}{x\left(x+1\right)} með því að margfalda teljara sinnum teljara og samnefnara sinnum samnefnara.
\frac{9\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)}{\left(x-2\right)\left(x+1\right)\times 4\left(2x+4\right)}
Deildu \frac{9}{\left(x-2\right)\left(x+1\right)} með \frac{4\left(2x+4\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)} með því að margfalda \frac{9}{\left(x-2\right)\left(x+1\right)} með umhverfu \frac{4\left(2x+4\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)}.
\frac{9x\left(x+1\right)\left(x+2\right)}{4\left(2x+4\right)}
Styttu burt \left(x-2\right)\left(x+1\right) í bæði teljara og samnefnara.
\frac{9x\left(x+1\right)\left(x+2\right)}{2\times 4\left(x+2\right)}
Þættaðu segðir sem hafa ekki þegar verið þættaðar.
\frac{9x\left(x+1\right)}{2\times 4}
Styttu burt x+2 í bæði teljara og samnefnara.
\frac{9x^{2}+9x}{8}
Víkkaðu segðina út.
\frac{\frac{\left(x-2\right)\left(x-2\right)}{\left(x-2\right)\left(x+1\right)}+\frac{\left(5-x\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
Til að leggja saman eða draga saman segðir skaltu stækka þær til að nefnararnir verði eins. Minnsta sameiginlega margfeldi x+1 og x-2 er \left(x-2\right)\left(x+1\right). Margfaldaðu \frac{x-2}{x+1} sinnum \frac{x-2}{x-2}. Margfaldaðu \frac{5-x}{x-2} sinnum \frac{x+1}{x+1}.
\frac{\frac{\left(x-2\right)\left(x-2\right)+\left(5-x\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
Þar sem \frac{\left(x-2\right)\left(x-2\right)}{\left(x-2\right)\left(x+1\right)} og \frac{\left(5-x\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)} eru með sama nefnara skaltu leggja saman með því að leggja saman teljarana.
\frac{\frac{x^{2}-2x-2x+4+5x+5-x^{2}-x}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
Margfaldaðu í \left(x-2\right)\left(x-2\right)+\left(5-x\right)\left(x+1\right).
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
Sameinaðu svipaða liði í x^{2}-2x-2x+4+5x+5-x^{2}-x.
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{\left(x-2\right)\left(x+1\right)}-\frac{1}{\left(x+1\right)\left(x+2\right)}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
Stuðull x^{2}-x-2. Stuðull x^{2}+3x+2.
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{x+2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}-\frac{x-2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
Til að leggja saman eða draga saman segðir skaltu stækka þær til að nefnararnir verði eins. Minnsta sameiginlega margfeldi \left(x-2\right)\left(x+1\right) og \left(x+1\right)\left(x+2\right) er \left(x-2\right)\left(x+1\right)\left(x+2\right). Margfaldaðu \frac{1}{\left(x-2\right)\left(x+1\right)} sinnum \frac{x+2}{x+2}. Margfaldaðu \frac{1}{\left(x+1\right)\left(x+2\right)} sinnum \frac{x-2}{x-2}.
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{x+2-\left(x-2\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
Þar sem \frac{x+2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)} og \frac{x-2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)} eru með sama nefnara skaltu draga frá með því að nota frádrátt á teljarana.
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{x+2-x+2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
Margfaldaðu í x+2-\left(x-2\right).
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}
Sameinaðu svipaða liði í x+2-x+2.
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x\left(x+1\right)}\right)}
Stuðull x^{2}+x.
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{\left(x+1\right)\left(x+1\right)}{x\left(x+1\right)}+\frac{3-x^{2}}{x\left(x+1\right)}\right)}
Til að leggja saman eða draga saman segðir skaltu stækka þær til að nefnararnir verði eins. Minnsta sameiginlega margfeldi x og x\left(x+1\right) er x\left(x+1\right). Margfaldaðu \frac{x+1}{x} sinnum \frac{x+1}{x+1}.
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\times \frac{\left(x+1\right)\left(x+1\right)+3-x^{2}}{x\left(x+1\right)}}
Þar sem \frac{\left(x+1\right)\left(x+1\right)}{x\left(x+1\right)} og \frac{3-x^{2}}{x\left(x+1\right)} eru með sama nefnara skaltu leggja saman með því að leggja saman teljarana.
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\times \frac{x^{2}+x+1+x+3-x^{2}}{x\left(x+1\right)}}
Margfaldaðu í \left(x+1\right)\left(x+1\right)+3-x^{2}.
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\times \frac{2x+4}{x\left(x+1\right)}}
Sameinaðu svipaða liði í x^{2}+x+1+x+3-x^{2}.
\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4\left(2x+4\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)}}
Margfaldaðu \frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)} sinnum \frac{2x+4}{x\left(x+1\right)} með því að margfalda teljara sinnum teljara og samnefnara sinnum samnefnara.
\frac{9\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)}{\left(x-2\right)\left(x+1\right)\times 4\left(2x+4\right)}
Deildu \frac{9}{\left(x-2\right)\left(x+1\right)} með \frac{4\left(2x+4\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)} með því að margfalda \frac{9}{\left(x-2\right)\left(x+1\right)} með umhverfu \frac{4\left(2x+4\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)}.
\frac{9x\left(x+1\right)\left(x+2\right)}{4\left(2x+4\right)}
Styttu burt \left(x-2\right)\left(x+1\right) í bæði teljara og samnefnara.
\frac{9x\left(x+1\right)\left(x+2\right)}{2\times 4\left(x+2\right)}
Þættaðu segðir sem hafa ekki þegar verið þættaðar.
\frac{9x\left(x+1\right)}{2\times 4}
Styttu burt x+2 í bæði teljara og samnefnara.
\frac{9x^{2}+9x}{8}
Víkkaðu segðina út.
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