f(x)=x-8/3x-4quada+x=2 eching

$$f ( x ) = \frac { x - 8 } { 3 x - 4 } \quad a + x = 2$$

a uchun yechish

$$a=-\frac{\left(x-2\right)\left(3x-4\right)}{x-8}$$

$$x\neq 8\text{ and }x\neq \frac{4}{3}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini 3x-4 ga ko'paytirish.

$$\left(x-8\right)a+\left(3x-4\right)x=2\left(3x-4\right)$$

x-8 ga a ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$xa-8a+\left(3x-4\right)x=2\left(3x-4\right)$$

3x-4 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$xa-8a+3x^{2}-4x=2\left(3x-4\right)$$

2 ga 3x-4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$xa-8a+3x^{2}-4x=6x-8$$

Ikkala tarafdan 3x^{2} ni ayirish.

$$xa-8a-4x=6x-8-3x^{2}$$

4x ni ikki tarafga qo’shing.

$$xa-8a=6x-8-3x^{2}+4x$$

10x ni olish uchun 6x va 4x ni birlashtirish.

$$xa-8a=10x-8-3x^{2}$$

a'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(x-8\right)a=10x-8-3x^{2}$$

Tenglama standart shaklda.

$$\left(x-8\right)a=-3x^{2}+10x-8$$

Ikki tarafini x-8 ga bo‘ling.

$$\frac{\left(x-8\right)a}{x-8}=\frac{\left(2-x\right)\left(3x-4\right)}{x-8}$$

x-8 ga bo'lish x-8 ga ko'paytirishni bekor qiladi.

$$a=\frac{\left(2-x\right)\left(3x-4\right)}{x-8}$$

x uchun yechish (complex solution)

$$\left\{\begin{matrix}\\x=\frac{\sqrt{a^{2}+76a+4}}{6}-\frac{a}{6}+\frac{5}{3}\text{, }&\text{unconditionally}\\x=-\frac{\sqrt{a^{2}+76a+4}}{6}-\frac{a}{6}+\frac{5}{3}\text{, }&a\neq 0\end{matrix}\right,$$

x uchun yechish

$$\left\{\begin{matrix}x=-\frac{\sqrt{a^{2}+76a+4}}{6}-\frac{a}{6}+\frac{5}{3}\text{, }&\left(a\neq 0\text{ and }a\geq 12\sqrt{10}-38\right)\text{ or }a\leq -12\sqrt{10}-38\\x=\frac{\sqrt{a^{2}+76a+4}}{6}-\frac{a}{6}+\frac{5}{3}\text{, }&a\geq 12\sqrt{10}-38\text{ or }a\leq -12\sqrt{10}-38\end{matrix}\right,$$