x/a-1=ax+4 eching

$$\frac { x } { a - 1 } = a x + 4$$

x uchun yechish

$$x=-\frac{4\left(1-a\right)}{1+a-a^{2}}$$

$$a\neq \frac{\sqrt{5}+1}{2}\text{ and }a\neq \frac{1-\sqrt{5}}{2}\text{ and }a\neq 1$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini a-1 ga ko'paytirish.

$$x=ax\left(a-1\right)+\left(a-1\right)\times 4$$

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

$$x=xa^{2}-ax+\left(a-1\right)\times 4$$

a-1 ga 4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x=xa^{2}-ax+4a-4$$

Ikkala tarafdan xa^{2} ni ayirish.

$$x-xa^{2}=-ax+4a-4$$

ax ni ikki tarafga qo’shing.

$$x-xa^{2}+ax=4a-4$$

Shartlarni qayta saralash.

$$ax-xa^{2}+x=4a-4$$

x'ga ega bo'lgan barcha shartlarni birlashtirish.

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

Tenglama standart shaklda.

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

Ikki tarafini 1-a^{2}+a ga bo‘ling.

$$\frac{\left(1+a-a^{2}\right)x}{1+a-a^{2}}=\frac{4a-4}{1+a-a^{2}}$$

1-a^{2}+a ga bo'lish 1-a^{2}+a ga ko'paytirishni bekor qiladi.

$$x=\frac{4a-4}{1+a-a^{2}}$$

-4+4a ni 1-a^{2}+a ga bo'lish.

$$x=\frac{4\left(a-1\right)}{1+a-a^{2}}$$

a uchun yechish

$$a=-\frac{\sqrt{5x^{2}+8x+16}-x+4}{2x}$$

$$a=-\frac{-\sqrt{5x^{2}+8x+16}-x+4}{2x}\text{, }x\neq 0$$