x/2k^2-2+1-2x/k^2-k-2=1/k^2-3k+2 eching

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

k uchun yechish (complex solution)

$$k=\frac{2}{3}-\frac{4}{3x}$$

$$x\neq \frac{4}{5}\text{ and }x\neq 0\text{ and }x\neq -4\text{ and }x\neq -1$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

k qiymati -1,1,2 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 2\left(k-2\right)\left(k-1\right)\left(k+1\right) ga, 2k^{2}-2,k^{2}-k-2,k^{2}-3k+2 ning eng kichik karralisiga ko‘paytiring.

$$\left(k-2\right)x+\left(2k-2\right)\left(1-2x\right)=2k+2$$

k-2 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$kx-2x+\left(2k-2\right)\left(1-2x\right)=2k+2$$

2k-2 ga 1-2x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$kx-2x+2k-4xk-2+4x=2k+2$$

-3kx ni olish uchun kx va -4xk ni birlashtirish.

$$-3kx-2x+2k-2+4x=2k+2$$

2x ni olish uchun -2x va 4x ni birlashtirish.

$$-3kx+2x+2k-2=2k+2$$

Ikkala tarafdan 2k ni ayirish.

$$-3kx+2x+2k-2-2k=2$$

0 ni olish uchun 2k va -2k ni birlashtirish.

$$-3kx+2x-2=2$$

Ikkala tarafdan 2x ni ayirish.

$$-3kx-2=2-2x$$

2 ni ikki tarafga qo’shing.

$$-3kx=2-2x+2$$

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

$$-3kx=4-2x$$

Tenglama standart shaklda.

$$\left(-3x\right)k=4-2x$$

Ikki tarafini -3x ga bo‘ling.

$$\frac{\left(-3x\right)k}{-3x}=\frac{4-2x}{-3x}$$

-3x ga bo'lish -3x ga ko'paytirishni bekor qiladi.

$$k=\frac{4-2x}{-3x}$$

4-2x ni -3x ga bo'lish.

$$k=\frac{2}{3}-\frac{4}{3x}$$

k qiymati -1,1,2 qiymatlaridan birortasiga teng bo‘lmaydi.

$$k=\frac{2}{3}-\frac{4}{3x}\text{, }k\neq -1\text{ and }k\neq 1\text{ and }k\neq 2$$

x uchun yechish (complex solution)

$$x=\frac{4}{2-3k}$$

$$k\neq \frac{2}{3}\text{ and }k\neq -1\text{ and }k\neq 1\text{ and }k\neq 2$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini 2\left(k-2\right)\left(k-1\right)\left(k+1\right) ga, 2k^{2}-2,k^{2}-k-2,k^{2}-3k+2 ning eng kichik karralisiga ko‘paytiring.

$$\left(k-2\right)x+\left(2k-2\right)\left(1-2x\right)=2k+2$$

k-2 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$kx-2x+\left(2k-2\right)\left(1-2x\right)=2k+2$$

2k-2 ga 1-2x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$kx-2x+2k-4kx-2+4x=2k+2$$

-3kx ni olish uchun kx va -4kx ni birlashtirish.

$$-3kx-2x+2k-2+4x=2k+2$$

2x ni olish uchun -2x va 4x ni birlashtirish.

$$-3kx+2x+2k-2=2k+2$$

Ikkala tarafdan 2k ni ayirish.

$$-3kx+2x-2=2k+2-2k$$

0 ni olish uchun 2k va -2k ni birlashtirish.

$$-3kx+2x-2=2$$

2 ni ikki tarafga qo’shing.

$$-3kx+2x=2+2$$

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

$$-3kx+2x=4$$

x'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(-3k+2\right)x=4$$

Tenglama standart shaklda.

$$\left(2-3k\right)x=4$$

Ikki tarafini 2-3k ga bo‘ling.

$$\frac{\left(2-3k\right)x}{2-3k}=\frac{4}{2-3k}$$

2-3k ga bo'lish 2-3k ga ko'paytirishni bekor qiladi.

$$x=\frac{4}{2-3k}$$

k uchun yechish

$$k=\frac{2}{3}-\frac{4}{3x}$$

$$x\neq -4\text{ and }x\neq 0\text{ and }x\neq \frac{4}{5}\text{ and }x\neq -1$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

k qiymati -1,1,2 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 2\left(k-2\right)\left(k-1\right)\left(k+1\right) ga, 2k^{2}-2,k^{2}-k-2,k^{2}-3k+2 ning eng kichik karralisiga ko‘paytiring.

$$\left(k-2\right)x+\left(2k-2\right)\left(1-2x\right)=2k+2$$

k-2 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$kx-2x+\left(2k-2\right)\left(1-2x\right)=2k+2$$

2k-2 ga 1-2x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$kx-2x+2k-4xk-2+4x=2k+2$$

-3kx ni olish uchun kx va -4xk ni birlashtirish.

$$-3kx-2x+2k-2+4x=2k+2$$

2x ni olish uchun -2x va 4x ni birlashtirish.

$$-3kx+2x+2k-2=2k+2$$

Ikkala tarafdan 2k ni ayirish.

$$-3kx+2x+2k-2-2k=2$$

0 ni olish uchun 2k va -2k ni birlashtirish.

$$-3kx+2x-2=2$$

Ikkala tarafdan 2x ni ayirish.

$$-3kx-2=2-2x$$

2 ni ikki tarafga qo’shing.

$$-3kx=2-2x+2$$

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

$$-3kx=4-2x$$

Tenglama standart shaklda.

$$\left(-3x\right)k=4-2x$$

Ikki tarafini -3x ga bo‘ling.

$$\frac{\left(-3x\right)k}{-3x}=\frac{4-2x}{-3x}$$

-3x ga bo'lish -3x ga ko'paytirishni bekor qiladi.

$$k=\frac{4-2x}{-3x}$$

4-2x ni -3x ga bo'lish.

$$k=\frac{2}{3}-\frac{4}{3x}$$

k qiymati -1,1,2 qiymatlaridan birortasiga teng bo‘lmaydi.

$$k=\frac{2}{3}-\frac{4}{3x}\text{, }k\neq -1\text{ and }k\neq 1\text{ and }k\neq 2$$

x uchun yechish

$$x=\frac{4}{2-3k}$$

$$k\neq \frac{2}{3}\text{ and }k\neq 2\text{ and }|k|\neq 1$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini 2\left(k-2\right)\left(k-1\right)\left(k+1\right) ga, 2k^{2}-2,k^{2}-k-2,k^{2}-3k+2 ning eng kichik karralisiga ko‘paytiring.

$$\left(k-2\right)x+\left(2k-2\right)\left(1-2x\right)=2k+2$$

k-2 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$kx-2x+\left(2k-2\right)\left(1-2x\right)=2k+2$$

2k-2 ga 1-2x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$kx-2x+2k-4kx-2+4x=2k+2$$

-3kx ni olish uchun kx va -4kx ni birlashtirish.

$$-3kx-2x+2k-2+4x=2k+2$$

2x ni olish uchun -2x va 4x ni birlashtirish.

$$-3kx+2x+2k-2=2k+2$$

Ikkala tarafdan 2k ni ayirish.

$$-3kx+2x-2=2k+2-2k$$

0 ni olish uchun 2k va -2k ni birlashtirish.

$$-3kx+2x-2=2$$

2 ni ikki tarafga qo’shing.

$$-3kx+2x=2+2$$

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

$$-3kx+2x=4$$

x'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(-3k+2\right)x=4$$

Tenglama standart shaklda.

$$\left(2-3k\right)x=4$$

Ikki tarafini 2-3k ga bo‘ling.

$$\frac{\left(2-3k\right)x}{2-3k}=\frac{4}{2-3k}$$

2-3k ga bo'lish 2-3k ga ko'paytirishni bekor qiladi.

$$x=\frac{4}{2-3k}$$