Atrisiniet (x-2/x+1+5-x/x-2):[(1/x^2-x-2-1/x^2+3x+2)*(frac{x+1}{x}+frac{3-x^2}{x^2+x})]

$$( \frac { x - 2 } { x + 1 } + \frac { 5 - x } { x - 2 } ) : [ ( \frac { 1 } { x ^ { 2 } - x - 2 } - \frac { 1 } { x ^ { 2 } + 3 x + 2 } ) \cdot ( \frac { x + 1 } { x } + \frac { 3 - x ^ { 2 } } { x ^ { 2 } + x } ) ]$$

Izrēķināt

$$\frac{9x\left(x+1\right)}{8}$$

Īsās risinājuma darbības

Lai saskaitītu vai atņemtu izteiksmes, izvērsiet tās, vienādojot saucējus. x+1 un x-2 mazākais kopējais skaitlis, ar kuru dalāms bez atlikuma, ir \left(x-2\right)\left(x+1\right). Reiziniet \frac{x-2}{x+1} reiz \frac{x-2}{x-2}. Reiziniet \frac{5-x}{x-2} reiz \frac{x+1}{x+1}.

$$\frac{\frac{\left(x-2\right)\left(x-2\right)}{\left(x-2\right)\left(x+1\right)}+\frac{\left(5-x\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

Tā kā \frac{\left(x-2\right)\left(x-2\right)}{\left(x-2\right)\left(x+1\right)} un \frac{\left(5-x\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)} ir viens un tas pats saucējs, saskaitiet tos, saskaitot to skaitītājus.

$$\frac{\frac{\left(x-2\right)\left(x-2\right)+\left(5-x\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

Veiciet reizināšanas darbības izteiksmē \left(x-2\right)\left(x-2\right)+\left(5-x\right)\left(x+1\right).

$$\frac{\frac{x^{2}-2x-2x+4+5x+5-x^{2}-x}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

Apvienojiet līdzīgos locekļus izteiksmē x^{2}-2x-2x+4+5x+5-x^{2}-x.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

Sadaliet reizinātājos x^{2}-x-2. Sadaliet reizinātājos x^{2}+3x+2.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{\left(x-2\right)\left(x+1\right)}-\frac{1}{\left(x+1\right)\left(x+2\right)}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

Lai saskaitītu vai atņemtu izteiksmes, izvērsiet tās, vienādojot saucējus. \left(x-2\right)\left(x+1\right) un \left(x+1\right)\left(x+2\right) mazākais kopējais skaitlis, ar kuru dalāms bez atlikuma, ir \left(x-2\right)\left(x+1\right)\left(x+2\right). Reiziniet \frac{1}{\left(x-2\right)\left(x+1\right)} reiz \frac{x+2}{x+2}. Reiziniet \frac{1}{\left(x+1\right)\left(x+2\right)} reiz \frac{x-2}{x-2}.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{x+2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}-\frac{x-2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

Tā kā \frac{x+2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)} un \frac{x-2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)} ir viens un tas pats saucējs, atņemiet tos, atņemot to skaitītājus.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{x+2-\left(x-2\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

Veiciet reizināšanas darbības izteiksmē x+2-\left(x-2\right).

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{x+2-x+2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

Apvienojiet līdzīgos locekļus izteiksmē x+2-x+2.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

Sadaliet reizinātājos x^{2}+x.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x\left(x+1\right)}\right)}$$

Lai saskaitītu vai atņemtu izteiksmes, izvērsiet tās, vienādojot saucējus. x un x\left(x+1\right) mazākais kopējais skaitlis, ar kuru dalāms bez atlikuma, ir x\left(x+1\right). Reiziniet \frac{x+1}{x} reiz \frac{x+1}{x+1}.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{\left(x+1\right)\left(x+1\right)}{x\left(x+1\right)}+\frac{3-x^{2}}{x\left(x+1\right)}\right)}$$

Tā kā \frac{\left(x+1\right)\left(x+1\right)}{x\left(x+1\right)} un \frac{3-x^{2}}{x\left(x+1\right)} ir viens un tas pats saucējs, saskaitiet tos, saskaitot to skaitītājus.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\times \frac{\left(x+1\right)\left(x+1\right)+3-x^{2}}{x\left(x+1\right)}}$$

Veiciet reizināšanas darbības izteiksmē \left(x+1\right)\left(x+1\right)+3-x^{2}.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\times \frac{x^{2}+x+1+x+3-x^{2}}{x\left(x+1\right)}}$$

Apvienojiet līdzīgos locekļus izteiksmē x^{2}+x+1+x+3-x^{2}.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\times \frac{2x+4}{x\left(x+1\right)}}$$

Reiziniet \frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)} ar \frac{2x+4}{x\left(x+1\right)}, reizinot skaitītāju ar skaitītāju un saucēju ar saucēju.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4\left(2x+4\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)}}$$

Daliet \frac{9}{\left(x-2\right)\left(x+1\right)} ar \frac{4\left(2x+4\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)}, reizinot \frac{9}{\left(x-2\right)\left(x+1\right)} ar apgriezto daļskaitli \frac{4\left(2x+4\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)} .

$$\frac{9\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)}{\left(x-2\right)\left(x+1\right)\times 4\left(2x+4\right)}$$

Saīsiniet \left(x-2\right)\left(x+1\right) gan skaitītājā, gan saucējā.

$$\frac{9x\left(x+1\right)\left(x+2\right)}{4\left(2x+4\right)}$$

Sadaliet reizinātājos izteiksmes, kas vēl nav sadalītas reizinātājos.

$$\frac{9x\left(x+1\right)\left(x+2\right)}{2\times 4\left(x+2\right)}$$

Saīsiniet x+2 gan skaitītājā, gan saucējā.

$$\frac{9x\left(x+1\right)}{2\times 4}$$

Izvērsiet izteiksmi.

$$\frac{9x^{2}+9x}{8}$$

Paplašināt

$$\frac{9x^{2}+9x}{8}$$

Īsās risinājuma darbības

Lai saskaitītu vai atņemtu izteiksmes, izvērsiet tās, vienādojot saucējus. x+1 un x-2 mazākais kopējais skaitlis, ar kuru dalāms bez atlikuma, ir \left(x-2\right)\left(x+1\right). Reiziniet \frac{x-2}{x+1} reiz \frac{x-2}{x-2}. Reiziniet \frac{5-x}{x-2} reiz \frac{x+1}{x+1}.

$$\frac{\frac{\left(x-2\right)\left(x-2\right)}{\left(x-2\right)\left(x+1\right)}+\frac{\left(5-x\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

Tā kā \frac{\left(x-2\right)\left(x-2\right)}{\left(x-2\right)\left(x+1\right)} un \frac{\left(5-x\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)} ir viens un tas pats saucējs, saskaitiet tos, saskaitot to skaitītājus.

$$\frac{\frac{\left(x-2\right)\left(x-2\right)+\left(5-x\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

Veiciet reizināšanas darbības izteiksmē \left(x-2\right)\left(x-2\right)+\left(5-x\right)\left(x+1\right).

$$\frac{\frac{x^{2}-2x-2x+4+5x+5-x^{2}-x}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

Apvienojiet līdzīgos locekļus izteiksmē x^{2}-2x-2x+4+5x+5-x^{2}-x.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

Sadaliet reizinātājos x^{2}-x-2. Sadaliet reizinātājos x^{2}+3x+2.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{\left(x-2\right)\left(x+1\right)}-\frac{1}{\left(x+1\right)\left(x+2\right)}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

Lai saskaitītu vai atņemtu izteiksmes, izvērsiet tās, vienādojot saucējus. \left(x-2\right)\left(x+1\right) un \left(x+1\right)\left(x+2\right) mazākais kopējais skaitlis, ar kuru dalāms bez atlikuma, ir \left(x-2\right)\left(x+1\right)\left(x+2\right). Reiziniet \frac{1}{\left(x-2\right)\left(x+1\right)} reiz \frac{x+2}{x+2}. Reiziniet \frac{1}{\left(x+1\right)\left(x+2\right)} reiz \frac{x-2}{x-2}.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{x+2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}-\frac{x-2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

Tā kā \frac{x+2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)} un \frac{x-2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)} ir viens un tas pats saucējs, atņemiet tos, atņemot to skaitītājus.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{x+2-\left(x-2\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

Veiciet reizināšanas darbības izteiksmē x+2-\left(x-2\right).

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{x+2-x+2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

Apvienojiet līdzīgos locekļus izteiksmē x+2-x+2.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

Sadaliet reizinātājos x^{2}+x.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x\left(x+1\right)}\right)}$$

Lai saskaitītu vai atņemtu izteiksmes, izvērsiet tās, vienādojot saucējus. x un x\left(x+1\right) mazākais kopējais skaitlis, ar kuru dalāms bez atlikuma, ir x\left(x+1\right). Reiziniet \frac{x+1}{x} reiz \frac{x+1}{x+1}.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{\left(x+1\right)\left(x+1\right)}{x\left(x+1\right)}+\frac{3-x^{2}}{x\left(x+1\right)}\right)}$$

Tā kā \frac{\left(x+1\right)\left(x+1\right)}{x\left(x+1\right)} un \frac{3-x^{2}}{x\left(x+1\right)} ir viens un tas pats saucējs, saskaitiet tos, saskaitot to skaitītājus.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\times \frac{\left(x+1\right)\left(x+1\right)+3-x^{2}}{x\left(x+1\right)}}$$

Veiciet reizināšanas darbības izteiksmē \left(x+1\right)\left(x+1\right)+3-x^{2}.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\times \frac{x^{2}+x+1+x+3-x^{2}}{x\left(x+1\right)}}$$

Apvienojiet līdzīgos locekļus izteiksmē x^{2}+x+1+x+3-x^{2}.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\times \frac{2x+4}{x\left(x+1\right)}}$$

Reiziniet \frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)} ar \frac{2x+4}{x\left(x+1\right)}, reizinot skaitītāju ar skaitītāju un saucēju ar saucēju.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4\left(2x+4\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)}}$$

Daliet \frac{9}{\left(x-2\right)\left(x+1\right)} ar \frac{4\left(2x+4\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)}, reizinot \frac{9}{\left(x-2\right)\left(x+1\right)} ar apgriezto daļskaitli \frac{4\left(2x+4\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)} .

$$\frac{9\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)}{\left(x-2\right)\left(x+1\right)\times 4\left(2x+4\right)}$$

Saīsiniet \left(x-2\right)\left(x+1\right) gan skaitītājā, gan saucējā.

$$\frac{9x\left(x+1\right)\left(x+2\right)}{4\left(2x+4\right)}$$

Sadaliet reizinātājos izteiksmes, kas vēl nav sadalītas reizinātājos.

$$\frac{9x\left(x+1\right)\left(x+2\right)}{2\times 4\left(x+2\right)}$$

Saīsiniet x+2 gan skaitītājā, gan saucējā.

$$\frac{9x\left(x+1\right)}{2\times 4}$$

Izvērsiet izteiksmi.

$$\frac{9x^{2}+9x}{8}$$