1/alpha+1+1/beta+1=beta+1+alpha+1/(alpha+1)(beta+1) eching

$$\frac { 1 } { \alpha + 1 } + \frac { 1 } { \beta + 1 } = \frac { \beta + 1 + \alpha + 1 } { ( \alpha + 1 ) ( \beta + 1 ) }$$

α uchun yechish

$$\alpha \neq -1$$

$$\beta \neq -1$$

Yechim qadamlari

\alpha qiymati -1 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(\alpha +1\right)\left(\beta +1\right) ga, \alpha +1,\beta +1,\left(\alpha +1\right)\left(\beta +1\right) ning eng kichik karralisiga ko‘paytiring.

$$\beta +1+\alpha +1=\beta +1+\alpha +1$$

2 olish uchun 1 va 1'ni qo'shing.

$$\beta +2+\alpha =\beta +1+\alpha +1$$

2 olish uchun 1 va 1'ni qo'shing.

$$\beta +2+\alpha =\beta +2+\alpha$$

Ikkala tarafdan \alpha ni ayirish.

$$\beta +2+\alpha -\alpha =\beta +2$$

0 ni olish uchun \alpha va -\alpha ni birlashtirish.

$$\beta +2=\beta +2$$

Shartlarni qayta saralash.

$$\text{true}$$

Bu har qanday \alpha uchun to‘g‘ri.

$$\alpha \in \mathrm{R}$$

\alpha qiymati -1 teng bo‘lmaydi.

$$\alpha \in \mathrm{R}\setminus -1$$

β uchun yechish

$$\beta \neq -1$$

$$\alpha \neq -1$$

Yechim qadamlari

\beta qiymati -1 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(\alpha +1\right)\left(\beta +1\right) ga, \alpha +1,\beta +1,\left(\alpha +1\right)\left(\beta +1\right) ning eng kichik karralisiga ko‘paytiring.

$$\beta +1+\alpha +1=\beta +1+\alpha +1$$

2 olish uchun 1 va 1'ni qo'shing.

$$\beta +2+\alpha =\beta +1+\alpha +1$$

2 olish uchun 1 va 1'ni qo'shing.

$$\beta +2+\alpha =\beta +2+\alpha$$

Ikkala tarafdan \beta ni ayirish.

$$\beta +2+\alpha -\beta =2+\alpha$$

0 ni olish uchun \beta va -\beta ni birlashtirish.

$$2+\alpha =2+\alpha$$

Shartlarni qayta saralash.

$$\text{true}$$

Bu har qanday \beta uchun to‘g‘ri.

$$\beta \in \mathrm{R}$$

\beta qiymati -1 teng bo‘lmaydi.

$$\beta \in \mathrm{R}\setminus -1$$