frac{operatorname{gy}x}{x+1}+x+1/x=13/6 eching

$$\frac { \operatorname { gy } x } { x + 1 } + \frac { x + 1 } { x } = \frac { 13 } { 6 }$$

g uchun yechish (complex solution)

$$\left\{\begin{matrix}g=\frac{\left(7x-6\right)\left(x+1\right)}{6yx^{2}}\text{, }&x\neq 0\text{ and }y\neq 0\text{ and }x\neq -1\\g\in \mathrm{C}\text{, }&x=\frac{6}{7}\text{ and }y=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini 6x\left(x+1\right) ga, x+1,x,6 ning eng kichik karralisiga ko‘paytiring.

$$6xgyx+\left(6x+6\right)\left(x+1\right)=13x\left(x+1\right)$$

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

$$6x^{2}gy+\left(6x+6\right)\left(x+1\right)=13x\left(x+1\right)$$

6x+6 ga x+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$6x^{2}gy+6x^{2}+12x+6=13x\left(x+1\right)$$

13x ga x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6x^{2}gy+6x^{2}+12x+6=13x^{2}+13x$$

Ikkala tarafdan 6x^{2} ni ayirish.

$$6x^{2}gy+12x+6=13x^{2}+13x-6x^{2}$$

7x^{2} ni olish uchun 13x^{2} va -6x^{2} ni birlashtirish.

$$6x^{2}gy+12x+6=7x^{2}+13x$$

Ikkala tarafdan 12x ni ayirish.

$$6x^{2}gy+6=7x^{2}+13x-12x$$

x ni olish uchun 13x va -12x ni birlashtirish.

$$6x^{2}gy+6=7x^{2}+x$$

Ikkala tarafdan 6 ni ayirish.

$$6x^{2}gy=7x^{2}+x-6$$

Tenglama standart shaklda.

$$6yx^{2}g=7x^{2}+x-6$$

Ikki tarafini 6x^{2}y ga bo‘ling.

$$\frac{6yx^{2}g}{6yx^{2}}=\frac{\left(7x-6\right)\left(x+1\right)}{6yx^{2}}$$

6x^{2}y ga bo'lish 6x^{2}y ga ko'paytirishni bekor qiladi.

$$g=\frac{\left(7x-6\right)\left(x+1\right)}{6yx^{2}}$$

g uchun yechish

$$\left\{\begin{matrix}g=\frac{\left(7x-6\right)\left(x+1\right)}{6yx^{2}}\text{, }&x\neq 0\text{ and }y\neq 0\text{ and }x\neq -1\\g\in \mathrm{R}\text{, }&x=\frac{6}{7}\text{ and }y=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini 6x\left(x+1\right) ga, x+1,x,6 ning eng kichik karralisiga ko‘paytiring.

$$6xgyx+\left(6x+6\right)\left(x+1\right)=13x\left(x+1\right)$$

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

$$6x^{2}gy+\left(6x+6\right)\left(x+1\right)=13x\left(x+1\right)$$

6x+6 ga x+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$6x^{2}gy+6x^{2}+12x+6=13x\left(x+1\right)$$

13x ga x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6x^{2}gy+6x^{2}+12x+6=13x^{2}+13x$$

Ikkala tarafdan 6x^{2} ni ayirish.

$$6x^{2}gy+12x+6=13x^{2}+13x-6x^{2}$$

7x^{2} ni olish uchun 13x^{2} va -6x^{2} ni birlashtirish.

$$6x^{2}gy+12x+6=7x^{2}+13x$$

Ikkala tarafdan 12x ni ayirish.

$$6x^{2}gy+6=7x^{2}+13x-12x$$

x ni olish uchun 13x va -12x ni birlashtirish.

$$6x^{2}gy+6=7x^{2}+x$$

Ikkala tarafdan 6 ni ayirish.

$$6x^{2}gy=7x^{2}+x-6$$

Tenglama standart shaklda.

$$6yx^{2}g=7x^{2}+x-6$$

Ikki tarafini 6x^{2}y ga bo‘ling.

$$\frac{6yx^{2}g}{6yx^{2}}=\frac{\left(7x-6\right)\left(x+1\right)}{6yx^{2}}$$

6x^{2}y ga bo'lish 6x^{2}y ga ko'paytirishni bekor qiladi.

$$g=\frac{\left(7x-6\right)\left(x+1\right)}{6yx^{2}}$$

x uchun yechish (complex solution)

$$\left\{\begin{matrix}x=-\frac{\sqrt{169-144gy}-13}{12gy+\sqrt{169-144gy}-13}\text{, }&y\neq 0\text{ and }g\neq 0\\x=\frac{\sqrt{169-144gy}+13}{12gy-\sqrt{169-144gy}-13}\text{, }&g\neq \frac{7}{6y}\text{ and }y\neq 0\text{ and }g\neq 0\\x=\frac{6}{7}\text{, }&y=0\text{ or }g=0\end{matrix}\right,$$

x uchun yechish

$$\left\{\begin{matrix}x=-\frac{\sqrt{169-144gy}-13}{12gy+\sqrt{169-144gy}-13}\text{, }&\left(g\neq 0\text{ and }g\geq \frac{169}{144y}\text{ and }y<0\right)\text{ or }\left(g\neq 0\text{ and }g\leq \frac{169}{144y}\text{ and }y>0\right)\text{ or }\left(g=\frac{169}{144y}\text{ and }y\neq 0\right)\\x=\frac{\sqrt{169-144gy}+13}{12gy-\sqrt{169-144gy}-13}\text{, }&\left(g\neq \frac{7}{6y}\text{ and }g\geq \frac{169}{144y}\text{ and }g\neq 0\text{ and }y<0\right)\text{ or }\left(g\neq \frac{7}{6y}\text{ and }g\leq \frac{169}{144y}\text{ and }g\neq 0\text{ and }y>0\right)\text{ or }\left(g=\frac{169}{144y}\text{ and }y\neq 0\right)\\x=12\text{, }&g=\frac{169}{144y}\text{ and }y\neq 0\\x=\frac{6}{7}\text{, }&y=0\text{ or }g=0\end{matrix}\right,$$