Riješi r+2/r(r+3)-r-1/r(r+2)

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

Izračunaj

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

Kratki koraci za rješenje

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva r\left(r+3\right) i r\left(r+2\right) jest r\left(r+2\right)\left(r+3\right). Pomnožite \frac{r+2}{r\left(r+3\right)} i \frac{r+2}{r+2}. Pomnožite \frac{r-1}{r\left(r+2\right)} i \frac{r+3}{r+3}.

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

Budući da \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)} imaju isti nazivnik, oduzmite ih oduzimanje njihovih brojnika.

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

Pomnožite izraz \left(r+2\right)\left(r+2\right)-\left(r-1\right)\left(r+3\right).

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

Kombinirajte slične izraze u r^{2}+2r+2r+4-r^{2}-3r+r+3.

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

Proširivanje broja r\left(r+2\right)\left(r+3\right).

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

Proširi

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

Kratki koraci za rješenje

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva r\left(r+3\right) i r\left(r+2\right) jest r\left(r+2\right)\left(r+3\right). Pomnožite \frac{r+2}{r\left(r+3\right)} i \frac{r+2}{r+2}. Pomnožite \frac{r-1}{r\left(r+2\right)} i \frac{r+3}{r+3}.

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

Budući da \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)} imaju isti nazivnik, oduzmite ih oduzimanje njihovih brojnika.

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

Pomnožite izraz \left(r+2\right)\left(r+2\right)-\left(r-1\right)\left(r+3\right).

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

Kombinirajte slične izraze u r^{2}+2r+2r+4-r^{2}-3r+r+3.

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

Proširivanje broja r\left(r+2\right)\left(r+3\right).

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