t^2-3/1-t^2+t+1/t-1=4/1+t eching

$$\frac { t ^ { 2 } - 3 } { 1 - t ^ { 2 } } + \frac { t + 1 } { t - 1 } = \frac { 4 } { 1 + t }$$

t uchun yechish

$$t=4$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$-\left(t^{2}-3\right)+\left(t+1\right)\left(t+1\right)=\left(t-1\right)\times 4$$

\left(t+1\right)^{2} hosil qilish uchun t+1 va t+1 ni ko'paytirish.

$$-\left(t^{2}-3\right)+\left(t+1\right)^{2}=\left(t-1\right)\times 4$$

t^{2}-3 teskarisini topish uchun har birining teskarisini toping.

$$-t^{2}+3+\left(t+1\right)^{2}=\left(t-1\right)\times 4$$

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

$$-t^{2}+3+t^{2}+2t+1=\left(t-1\right)\times 4$$

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

$$3+2t+1=\left(t-1\right)\times 4$$

4 olish uchun 3 va 1'ni qo'shing.

$$4+2t=\left(t-1\right)\times 4$$

t-1 ga 4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4+2t=4t-4$$

Ikkala tarafdan 4t ni ayirish.

$$4+2t-4t=-4$$

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

$$4-2t=-4$$

Ikkala tarafdan 4 ni ayirish.

$$-2t=-4-4$$

-8 olish uchun -4 dan 4 ni ayirish.

$$-2t=-8$$

Ikki tarafini -2 ga bo‘ling.

$$t=\frac{-8}{-2}$$

4 ni olish uchun -8 ni -2 ga bo‘ling.

$$t=4$$