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

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

m uchun yechish

$$m=0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

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

\left(m-1\right)^{2} hosil qilish uchun m-1 va m-1 ni ko'paytirish.

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

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(m-1\right)^{2} kengaytirilishi uchun ishlating.

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

m+1 ga 2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

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

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

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

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

-m^{2} ni olish uchun m^{2} va -2m^{2} ni birlashtirish.

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

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

$$-m^{2}-4m+1=-\left(m-1\right)\left(m+1\right)$$

-1 ga m-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-m^{2}-4m+1=\left(-m+1\right)\left(m+1\right)$$

-m+1 ga m+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$-m^{2}-4m+1=-m^{2}+1$$

m^{2} ni ikki tarafga qo’shing.

$$-m^{2}-4m+1+m^{2}=1$$

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

$$-4m+1=1$$

Ikkala tarafdan 1 ni ayirish.

$$-4m=1-1$$

0 olish uchun 1 dan 1 ni ayirish.

$$-4m=0$$

Ikki son koʻpaytmasi 0 ga teng, agar kamida bittasi 0 bo‘lsa. -4 0 ga teng bo‘lmasa, m 0 ga teng bo‘lishi kerak.

$$m=0$$