Evaluer
\frac{9x\left(x+1\right)}{8}
Udvid
\frac{9x^{2}+9x}{8}
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\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)}
For tilføje eller fratrække udtryk skal du udvide dem for at gøre nævneren ens. Mindste fælles multiplum for x+1 og x-2 er \left(x-2\right)\left(x+1\right). Multiplicer \frac{x-2}{x+1} gange \frac{x-2}{x-2}. Multiplicer \frac{5-x}{x-2} gange \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)}
Da \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)} har den samme fællesnævner, skal du addere dem ved at tilføje deres tællere.
\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)}
Lav multiplikationerne i \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)}
Kombiner ens led i 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)}
Faktoriser x^{2}-x-2. Faktoriser 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)}
For tilføje eller fratrække udtryk skal du udvide dem for at gøre nævneren ens. Mindste fælles multiplum for \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). Multiplicer \frac{1}{\left(x-2\right)\left(x+1\right)} gange \frac{x+2}{x+2}. Multiplicer \frac{1}{\left(x+1\right)\left(x+2\right)} gange \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)}
Eftersom \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)} har den samme fællesnævner, kan du trække dem fra dem ved at trække deres tællere fra.
\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)}
Lav multiplikationerne i 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)}
Kombiner ens led i 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)}
Faktoriser 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)}
For tilføje eller fratrække udtryk skal du udvide dem for at gøre nævneren ens. Mindste fælles multiplum for x og x\left(x+1\right) er x\left(x+1\right). Multiplicer \frac{x+1}{x} gange \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)}}
Da \frac{\left(x+1\right)\left(x+1\right)}{x\left(x+1\right)} og \frac{3-x^{2}}{x\left(x+1\right)} har den samme fællesnævner, skal du addere dem ved at tilføje deres tællere.
\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)}}
Lav multiplikationerne i \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)}}
Kombiner ens led i 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)}}
Multiplicer \frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)} gange \frac{2x+4}{x\left(x+1\right)} ved at multiplicere tæller gange tæller og nævner gange nævner.
\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)}
Divider \frac{9}{\left(x-2\right)\left(x+1\right)} med \frac{4\left(2x+4\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)} ved at multiplicere \frac{9}{\left(x-2\right)\left(x+1\right)} med den reciprokke værdi af \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)}
Udlign \left(x-2\right)\left(x+1\right) i både tælleren og nævneren.
\frac{9x\left(x+1\right)\left(x+2\right)}{2\times 4\left(x+2\right)}
Faktoriser de udtryk, der ikke allerede er faktoriseret.
\frac{9x\left(x+1\right)}{2\times 4}
Udlign x+2 i både tælleren og nævneren.
\frac{9x^{2}+9x}{8}
Udvid udtrykket.
\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)}
For tilføje eller fratrække udtryk skal du udvide dem for at gøre nævneren ens. Mindste fælles multiplum for x+1 og x-2 er \left(x-2\right)\left(x+1\right). Multiplicer \frac{x-2}{x+1} gange \frac{x-2}{x-2}. Multiplicer \frac{5-x}{x-2} gange \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)}
Da \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)} har den samme fællesnævner, skal du addere dem ved at tilføje deres tællere.
\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)}
Lav multiplikationerne i \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)}
Kombiner ens led i 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)}
Faktoriser x^{2}-x-2. Faktoriser 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)}
For tilføje eller fratrække udtryk skal du udvide dem for at gøre nævneren ens. Mindste fælles multiplum for \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). Multiplicer \frac{1}{\left(x-2\right)\left(x+1\right)} gange \frac{x+2}{x+2}. Multiplicer \frac{1}{\left(x+1\right)\left(x+2\right)} gange \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)}
Eftersom \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)} har den samme fællesnævner, kan du trække dem fra dem ved at trække deres tællere fra.
\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)}
Lav multiplikationerne i 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)}
Kombiner ens led i 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)}
Faktoriser 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)}
For tilføje eller fratrække udtryk skal du udvide dem for at gøre nævneren ens. Mindste fælles multiplum for x og x\left(x+1\right) er x\left(x+1\right). Multiplicer \frac{x+1}{x} gange \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)}}
Da \frac{\left(x+1\right)\left(x+1\right)}{x\left(x+1\right)} og \frac{3-x^{2}}{x\left(x+1\right)} har den samme fællesnævner, skal du addere dem ved at tilføje deres tællere.
\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)}}
Lav multiplikationerne i \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)}}
Kombiner ens led i 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)}}
Multiplicer \frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)} gange \frac{2x+4}{x\left(x+1\right)} ved at multiplicere tæller gange tæller og nævner gange nævner.
\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)}
Divider \frac{9}{\left(x-2\right)\left(x+1\right)} med \frac{4\left(2x+4\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)} ved at multiplicere \frac{9}{\left(x-2\right)\left(x+1\right)} med den reciprokke værdi af \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)}
Udlign \left(x-2\right)\left(x+1\right) i både tælleren og nævneren.
\frac{9x\left(x+1\right)\left(x+2\right)}{2\times 4\left(x+2\right)}
Faktoriser de udtryk, der ikke allerede er faktoriseret.
\frac{9x\left(x+1\right)}{2\times 4}
Udlign x+2 i både tælleren og nævneren.
\frac{9x^{2}+9x}{8}
Udvid udtrykket.
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