Selesaikan x/x^2+3x+2+2x-3/1x^2-1

$$\frac { x } { x ^ { 2 } + 3 x + 2 } + \frac { 2 x - 3 } { 1 x ^ { 2 } - 1 }$$

Nilaikan

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

Langkah Penyelesaian Pendek

Faktor x^{2}+3x+2. Faktor 1x^{2}-1.

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

Untuk menambah atau menolak ungkapan, kembangkannya untuk membuat penyebut mereka sama. Gandaan sepunya terkecil \left(x+1\right)\left(x+2\right) dan \left(x-1\right)\left(x+1\right) ialah \left(x-1\right)\left(x+1\right)\left(x+2\right). Darabkan \frac{x}{\left(x+1\right)\left(x+2\right)} kali \frac{x-1}{x-1}. Darabkan \frac{2x-3}{\left(x-1\right)\left(x+1\right)} kali \frac{x+2}{x+2}.

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

Oleh kerana \frac{x\left(x-1\right)}{\left(x-1\right)\left(x+1\right)\left(x+2\right)} dan \frac{\left(2x-3\right)\left(x+2\right)}{\left(x-1\right)\left(x+1\right)\left(x+2\right)} mempunyai penyebut yang sama, tambahkan dengan menambahkan pengangka.

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

Lakukan pendaraban dalam x\left(x-1\right)+\left(2x-3\right)\left(x+2\right).

$$\frac{x^{2}-x+2x^{2}+4x-3x-6}{\left(x-1\right)\left(x+1\right)\left(x+2\right)}$$

Gabungkan sebutan serupa dalam x^{2}-x+2x^{2}+4x-3x-6.

$$\frac{3x^{2}-6}{\left(x-1\right)\left(x+1\right)\left(x+2\right)}$$

Kembangkan \left(x-1\right)\left(x+1\right)\left(x+2\right).

$$\frac{3x^{2}-6}{x^{3}+2x^{2}-x-2}$$

Kembangkan

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

Langkah Penyelesaian Pendek

Faktor x^{2}+3x+2. Faktor 1x^{2}-1.

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

Untuk menambah atau menolak ungkapan, kembangkannya untuk membuat penyebut mereka sama. Gandaan sepunya terkecil \left(x+1\right)\left(x+2\right) dan \left(x-1\right)\left(x+1\right) ialah \left(x-1\right)\left(x+1\right)\left(x+2\right). Darabkan \frac{x}{\left(x+1\right)\left(x+2\right)} kali \frac{x-1}{x-1}. Darabkan \frac{2x-3}{\left(x-1\right)\left(x+1\right)} kali \frac{x+2}{x+2}.

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

Oleh kerana \frac{x\left(x-1\right)}{\left(x-1\right)\left(x+1\right)\left(x+2\right)} dan \frac{\left(2x-3\right)\left(x+2\right)}{\left(x-1\right)\left(x+1\right)\left(x+2\right)} mempunyai penyebut yang sama, tambahkan dengan menambahkan pengangka.

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

Lakukan pendaraban dalam x\left(x-1\right)+\left(2x-3\right)\left(x+2\right).

$$\frac{x^{2}-x+2x^{2}+4x-3x-6}{\left(x-1\right)\left(x+1\right)\left(x+2\right)}$$

Gabungkan sebutan serupa dalam x^{2}-x+2x^{2}+4x-3x-6.

$$\frac{3x^{2}-6}{\left(x-1\right)\left(x+1\right)\left(x+2\right)}$$

Kembangkan \left(x-1\right)\left(x+1\right)\left(x+2\right).

$$\frac{3x^{2}-6}{x^{3}+2x^{2}-x-2}$$