Los r+2/r(r+3)-r-1/r(r+2) op

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

Evalueren

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

Korte oplossingsstappen

Vouw expressies uit en maak de bijbehorende noemers gelijk om expressies op te tellen of af te trekken. Kleinste gemene veelvoud van r\left(r+3\right) en r\left(r+2\right) is r\left(r+2\right)\left(r+3\right). Vermenigvuldig \frac{r+2}{r\left(r+3\right)} met \frac{r+2}{r+2}. Vermenigvuldig \frac{r-1}{r\left(r+2\right)} met \frac{r+3}{r+3}.

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

Aangezien \frac{\left(r+2\right)\left(r+2\right)}{r\left(r+2\right)\left(r+3\right)} en \frac{\left(r-1\right)\left(r+3\right)}{r\left(r+2\right)\left(r+3\right)} dezelfde noemer hebben, kunt u ze aftrekken door hun tellers af te trekken.

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

Voer de vermenigvuldigingen uit in \left(r+2\right)\left(r+2\right)-\left(r-1\right)\left(r+3\right).

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

Combineer gelijke termen in r^{2}+2r+2r+4-r^{2}-3r+r+3.

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

Breid r\left(r+2\right)\left(r+3\right) uit.

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

Uitbreiden

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

Korte oplossingsstappen

Vouw expressies uit en maak de bijbehorende noemers gelijk om expressies op te tellen of af te trekken. Kleinste gemene veelvoud van r\left(r+3\right) en r\left(r+2\right) is r\left(r+2\right)\left(r+3\right). Vermenigvuldig \frac{r+2}{r\left(r+3\right)} met \frac{r+2}{r+2}. Vermenigvuldig \frac{r-1}{r\left(r+2\right)} met \frac{r+3}{r+3}.

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

Aangezien \frac{\left(r+2\right)\left(r+2\right)}{r\left(r+2\right)\left(r+3\right)} en \frac{\left(r-1\right)\left(r+3\right)}{r\left(r+2\right)\left(r+3\right)} dezelfde noemer hebben, kunt u ze aftrekken door hun tellers af te trekken.

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

Voer de vermenigvuldigingen uit in \left(r+2\right)\left(r+2\right)-\left(r-1\right)\left(r+3\right).

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

Combineer gelijke termen in r^{2}+2r+2r+4-r^{2}-3r+r+3.

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

Breid r\left(r+2\right)\left(r+3\right) uit.

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