Rešite r+2/r(r+3)-r-1/r(r+2)

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

Ovrednoti

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

Kratka navodila za rešitev

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik r\left(r+3\right) in r\left(r+2\right) je r\left(r+2\right)\left(r+3\right). Pomnožite \frac{r+2}{r\left(r+3\right)} s/z \frac{r+2}{r+2}. Pomnožite \frac{r-1}{r\left(r+2\right)} s/z \frac{r+3}{r+3}.

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

Ker \frac{\left(r+2\right)\left(r+2\right)}{r\left(r+2\right)\left(r+3\right)} in \frac{\left(r-1\right)\left(r+3\right)}{r\left(r+2\right)\left(r+3\right)} imata isti imenovalec, jih odštejte tako, da odštejete njihove števce.

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

Izvedi množenje v \left(r+2\right)\left(r+2\right)-\left(r-1\right)\left(r+3\right).

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

Združite podobne člene v r^{2}+2r+2r+4-r^{2}-3r+r+3.

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

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

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

Razširi

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

Kratka navodila za rešitev

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik r\left(r+3\right) in r\left(r+2\right) je r\left(r+2\right)\left(r+3\right). Pomnožite \frac{r+2}{r\left(r+3\right)} s/z \frac{r+2}{r+2}. Pomnožite \frac{r-1}{r\left(r+2\right)} s/z \frac{r+3}{r+3}.

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

Ker \frac{\left(r+2\right)\left(r+2\right)}{r\left(r+2\right)\left(r+3\right)} in \frac{\left(r-1\right)\left(r+3\right)}{r\left(r+2\right)\left(r+3\right)} imata isti imenovalec, jih odštejte tako, da odštejete njihove števce.

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

Izvedi množenje v \left(r+2\right)\left(r+2\right)-\left(r-1\right)\left(r+3\right).

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

Združite podobne člene v r^{2}+2r+2r+4-r^{2}-3r+r+3.

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

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

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