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

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

Evaluasi

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

Langkah-langkah Solusi Singkat

Untuk menambahkan atau mengurangi ekspresi, perluas untuk menyamakan penyebutnya. Kelipatan persekutuan terkecil dari r\left(r+3\right) dan r\left(r+2\right) adalah r\left(r+2\right)\left(r+3\right). Kalikan \frac{r+2}{r\left(r+3\right)} kali \frac{r+2}{r+2}. Kalikan \frac{r-1}{r\left(r+2\right)} kali \frac{r+3}{r+3}.

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

Karena \frac{\left(r+2\right)\left(r+2\right)}{r\left(r+2\right)\left(r+3\right)} dan \frac{\left(r-1\right)\left(r+3\right)}{r\left(r+2\right)\left(r+3\right)} memiliki penyebut yang sama, kurangi bilangan dengan mengurangkan pembilangnya.

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

Kalikan bilangan berikut \left(r+2\right)\left(r+2\right)-\left(r-1\right)\left(r+3\right).

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

Gabungkan seperti suku di r^{2}+2r+2r+4-r^{2}-3r+r+3.

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

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

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

Luaskan

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

Langkah-langkah Solusi Singkat

Untuk menambahkan atau mengurangi ekspresi, perluas untuk menyamakan penyebutnya. Kelipatan persekutuan terkecil dari r\left(r+3\right) dan r\left(r+2\right) adalah r\left(r+2\right)\left(r+3\right). Kalikan \frac{r+2}{r\left(r+3\right)} kali \frac{r+2}{r+2}. Kalikan \frac{r-1}{r\left(r+2\right)} kali \frac{r+3}{r+3}.

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

Karena \frac{\left(r+2\right)\left(r+2\right)}{r\left(r+2\right)\left(r+3\right)} dan \frac{\left(r-1\right)\left(r+3\right)}{r\left(r+2\right)\left(r+3\right)} memiliki penyebut yang sama, kurangi bilangan dengan mengurangkan pembilangnya.

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

Kalikan bilangan berikut \left(r+2\right)\left(r+2\right)-\left(r-1\right)\left(r+3\right).

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

Gabungkan seperti suku di r^{2}+2r+2r+4-r^{2}-3r+r+3.

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

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

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