xy=x+1/x5 eching

$$x y = \frac { x + 1 } { x } 5$$

y uchun yechish

$$y=\frac{5\left(x+1\right)}{x^{2}}$$

$$x\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini x ga ko'paytirish.

$$xyx=\left(x+1\right)\times 5$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$x^{2}y=\left(x+1\right)\times 5$$

x+1 ga 5 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}y=5x+5$$

Ikki tarafini x^{2} ga bo‘ling.

$$\frac{x^{2}y}{x^{2}}=\frac{5x+5}{x^{2}}$$

x^{2} ga bo'lish x^{2} ga ko'paytirishni bekor qiladi.

$$y=\frac{5x+5}{x^{2}}$$

5+5x ni x^{2} ga bo'lish.

$$y=\frac{5\left(x+1\right)}{x^{2}}$$

x uchun yechish (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{20y+25}+5}{2y}\text{; }x=\frac{-\sqrt{20y+25}+5}{2y}\text{, }&y\neq 0\\x=-1\text{, }&y=0\end{matrix}\right,$$

x uchun yechish

$$\left\{\begin{matrix}x=\frac{\sqrt{20y+25}+5}{2y}\text{; }x=\frac{-\sqrt{20y+25}+5}{2y}\text{, }&y\neq 0\text{ and }y\geq -\frac{5}{4}\\x=-1\text{, }&y=0\end{matrix}\right,$$