Atrisiniet r+2/r(r+3)-r-1/r(r+2)

$$\frac { r + 2 } { r ( r + 3 ) } - \frac { r - 1 } { r ( r + 2 ) }$$

Izrēķināt

$$\frac{2r+7}{r\left(r+2\right)\left(r+3\right)}$$

Īsās risinājuma darbības

Lai saskaitītu vai atņemtu izteiksmes, izvērsiet tās, vienādojot saucējus. r\left(r+3\right) un r\left(r+2\right) mazākais kopējais skaitlis, ar kuru dalāms bez atlikuma, ir r\left(r+2\right)\left(r+3\right). Reiziniet \frac{r+2}{r\left(r+3\right)} reiz \frac{r+2}{r+2}. Reiziniet \frac{r-1}{r\left(r+2\right)} reiz \frac{r+3}{r+3}.

$$\frac{\left(r+2\right)\left(r+2\right)}{r\left(r+2\right)\left(r+3\right)}-\frac{\left(r-1\right)\left(r+3\right)}{r\left(r+2\right)\left(r+3\right)}$$

Tā kā \frac{\left(r+2\right)\left(r+2\right)}{r\left(r+2\right)\left(r+3\right)} un \frac{\left(r-1\right)\left(r+3\right)}{r\left(r+2\right)\left(r+3\right)} ir viens un tas pats saucējs, atņemiet tos, atņemot to skaitītājus.

$$\frac{\left(r+2\right)\left(r+2\right)-\left(r-1\right)\left(r+3\right)}{r\left(r+2\right)\left(r+3\right)}$$

Veiciet reizināšanas darbības izteiksmē \left(r+2\right)\left(r+2\right)-\left(r-1\right)\left(r+3\right).

$$\frac{r^{2}+2r+2r+4-r^{2}-3r+r+3}{r\left(r+2\right)\left(r+3\right)}$$

Apvienojiet līdzīgos locekļus izteiksmē r^{2}+2r+2r+4-r^{2}-3r+r+3.

$$\frac{2r+7}{r\left(r+2\right)\left(r+3\right)}$$

Paplašiniet r\left(r+2\right)\left(r+3\right).

$$\frac{2r+7}{r^{3}+5r^{2}+6r}$$

Paplašināt

$$\frac{2r+7}{r\left(r+2\right)\left(r+3\right)}$$

Īsās risinājuma darbības

Lai saskaitītu vai atņemtu izteiksmes, izvērsiet tās, vienādojot saucējus. r\left(r+3\right) un r\left(r+2\right) mazākais kopējais skaitlis, ar kuru dalāms bez atlikuma, ir r\left(r+2\right)\left(r+3\right). Reiziniet \frac{r+2}{r\left(r+3\right)} reiz \frac{r+2}{r+2}. Reiziniet \frac{r-1}{r\left(r+2\right)} reiz \frac{r+3}{r+3}.

$$\frac{\left(r+2\right)\left(r+2\right)}{r\left(r+2\right)\left(r+3\right)}-\frac{\left(r-1\right)\left(r+3\right)}{r\left(r+2\right)\left(r+3\right)}$$

Tā kā \frac{\left(r+2\right)\left(r+2\right)}{r\left(r+2\right)\left(r+3\right)} un \frac{\left(r-1\right)\left(r+3\right)}{r\left(r+2\right)\left(r+3\right)} ir viens un tas pats saucējs, atņemiet tos, atņemot to skaitītājus.

$$\frac{\left(r+2\right)\left(r+2\right)-\left(r-1\right)\left(r+3\right)}{r\left(r+2\right)\left(r+3\right)}$$

Veiciet reizināšanas darbības izteiksmē \left(r+2\right)\left(r+2\right)-\left(r-1\right)\left(r+3\right).

$$\frac{r^{2}+2r+2r+4-r^{2}-3r+r+3}{r\left(r+2\right)\left(r+3\right)}$$

Apvienojiet līdzīgos locekļus izteiksmē r^{2}+2r+2r+4-r^{2}-3r+r+3.

$$\frac{2r+7}{r\left(r+2\right)\left(r+3\right)}$$

Paplašiniet r\left(r+2\right)\left(r+3\right).

$$\frac{2r+7}{r^{3}+5r^{2}+6r}$$