Lös r+2/r(r+3)-r-1/r(r+2)

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

Beräkna

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

Steg för kort lösning

Om du vill addera eller subtrahera uttryck expanderar du dem för att göra deras nämnare samma. Minsta gemensamma multipel av r\left(r+3\right) och r\left(r+2\right) är r\left(r+2\right)\left(r+3\right). Multiplicera \frac{r+2}{r\left(r+3\right)} med \frac{r+2}{r+2}. Multiplicera \frac{r-1}{r\left(r+2\right)} med \frac{r+3}{r+3}.

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

Eftersom \frac{\left(r+2\right)\left(r+2\right)}{r\left(r+2\right)\left(r+3\right)} och \frac{\left(r-1\right)\left(r+3\right)}{r\left(r+2\right)\left(r+3\right)} har samma nämnare subtraherar du dem genom att subtrahera deras täljare.

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

Gör multiplikationerna i \left(r+2\right)\left(r+2\right)-\left(r-1\right)\left(r+3\right).

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

Kombinera lika termer i r^{2}+2r+2r+4-r^{2}-3r+r+3.

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

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

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

Utveckla

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

Steg för kort lösning

Om du vill addera eller subtrahera uttryck expanderar du dem för att göra deras nämnare samma. Minsta gemensamma multipel av r\left(r+3\right) och r\left(r+2\right) är r\left(r+2\right)\left(r+3\right). Multiplicera \frac{r+2}{r\left(r+3\right)} med \frac{r+2}{r+2}. Multiplicera \frac{r-1}{r\left(r+2\right)} med \frac{r+3}{r+3}.

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

Eftersom \frac{\left(r+2\right)\left(r+2\right)}{r\left(r+2\right)\left(r+3\right)} och \frac{\left(r-1\right)\left(r+3\right)}{r\left(r+2\right)\left(r+3\right)} har samma nämnare subtraherar du dem genom att subtrahera deras täljare.

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

Gör multiplikationerna i \left(r+2\right)\left(r+2\right)-\left(r-1\right)\left(r+3\right).

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

Kombinera lika termer i r^{2}+2r+2r+4-r^{2}-3r+r+3.

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

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

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