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

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

Calcula

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

Passos de solució senzills

Per afegir o restar les expressions, amplieu-les perquè els denominadors coincideixin. El mínim comú múltiple de r\left(r+3\right) i r\left(r+2\right) és r\left(r+2\right)\left(r+3\right). Multipliqueu \frac{r+2}{r\left(r+3\right)} per \frac{r+2}{r+2}. Multipliqueu \frac{r-1}{r\left(r+2\right)} per \frac{r+3}{r+3}.

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

Com que \frac{\left(r+2\right)\left(r+2\right)}{r\left(r+2\right)\left(r+3\right)} i \frac{\left(r-1\right)\left(r+3\right)}{r\left(r+2\right)\left(r+3\right)} tenen el mateix denominador, resteu-los mitjançant la subtracció dels seus numeradors.

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

Feu les multiplicacions a \left(r+2\right)\left(r+2\right)-\left(r-1\right)\left(r+3\right).

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

Combineu els termes similars de r^{2}+2r+2r+4-r^{2}-3r+r+3.

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

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

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

Expandiu

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

Passos de solució senzills

Per afegir o restar les expressions, amplieu-les perquè els denominadors coincideixin. El mínim comú múltiple de r\left(r+3\right) i r\left(r+2\right) és r\left(r+2\right)\left(r+3\right). Multipliqueu \frac{r+2}{r\left(r+3\right)} per \frac{r+2}{r+2}. Multipliqueu \frac{r-1}{r\left(r+2\right)} per \frac{r+3}{r+3}.

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

Com que \frac{\left(r+2\right)\left(r+2\right)}{r\left(r+2\right)\left(r+3\right)} i \frac{\left(r-1\right)\left(r+3\right)}{r\left(r+2\right)\left(r+3\right)} tenen el mateix denominador, resteu-los mitjançant la subtracció dels seus numeradors.

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

Feu les multiplicacions a \left(r+2\right)\left(r+2\right)-\left(r-1\right)\left(r+3\right).

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

Combineu els termes similars de r^{2}+2r+2r+4-r^{2}-3r+r+3.

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

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

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