x+1/x+2-x/x-1=m/x^2+x-2 eching

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

x uchun yechish (complex solution)

$$x=\frac{-m-1}{2}$$

$$m\neq 3\text{ and }m\neq -3$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

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

Hisoblang: \left(x-1\right)\left(x+1\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 1 kvadratini chiqarish.

$$x^{2}-1-\left(x+2\right)x=m$$

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

$$x^{2}-1-\left(x^{2}+2x\right)=m$$

x^{2}+2x teskarisini topish uchun har birining teskarisini toping.

$$x^{2}-1-x^{2}-2x=m$$

0 ni olish uchun x^{2} va -x^{2} ni birlashtirish.

$$-1-2x=m$$

1 ni ikki tarafga qo’shing.

$$-2x=m+1$$

Ikki tarafini -2 ga bo‘ling.

$$\frac{-2x}{-2}=\frac{m+1}{-2}$$

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

$$x=\frac{m+1}{-2}$$

m+1 ni -2 ga bo'lish.

$$x=\frac{-m-1}{2}$$

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

$$x=\frac{-m-1}{2}\text{, }x\neq -2\text{ and }x\neq 1$$

m uchun yechish

$$m=-2x-1$$

$$x\neq -2\text{ and }x\neq 1$$

Yechim qadamlari

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

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

Hisoblang: \left(x-1\right)\left(x+1\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 1 kvadratini chiqarish.

$$x^{2}-1-\left(x+2\right)x=m$$

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

$$x^{2}-1-\left(x^{2}+2x\right)=m$$

x^{2}+2x teskarisini topish uchun har birining teskarisini toping.

$$x^{2}-1-x^{2}-2x=m$$

0 ni olish uchun x^{2} va -x^{2} ni birlashtirish.

$$-1-2x=m$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$m=-1-2x$$

x uchun yechish

$$x=\frac{-m-1}{2}$$

$$|m|\neq 3$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

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

Hisoblang: \left(x-1\right)\left(x+1\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 1 kvadratini chiqarish.

$$x^{2}-1-\left(x+2\right)x=m$$

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

$$x^{2}-1-\left(x^{2}+2x\right)=m$$

x^{2}+2x teskarisini topish uchun har birining teskarisini toping.

$$x^{2}-1-x^{2}-2x=m$$

0 ni olish uchun x^{2} va -x^{2} ni birlashtirish.

$$-1-2x=m$$

1 ni ikki tarafga qo’shing.

$$-2x=m+1$$

Ikki tarafini -2 ga bo‘ling.

$$\frac{-2x}{-2}=\frac{m+1}{-2}$$

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

$$x=\frac{m+1}{-2}$$

m+1 ni -2 ga bo'lish.

$$x=\frac{-m-1}{2}$$

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

$$x=\frac{-m-1}{2}\text{, }x\neq -2\text{ and }x\neq 1$$