3x/5+4/x-2x/y=2 eching

$$\frac { 3 x } { 5 } + \frac { 4 } { x } - \frac { 2 x } { y } = 2$$

y uchun yechish (complex solution)

$$y=-\frac{10x^{2}}{-3x^{2}+10x-20}$$

$$x\neq 0\text{ and }x\neq \frac{5+\sqrt{35}i}{3}\text{ and }x\neq \frac{-\sqrt{35}i+5}{3}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

y qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 5xy ga, 5,x,y ning eng kichik karralisiga ko‘paytiring.

$$xy\times 3x+5y\times 4-5x\times 2x=10xy$$

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

$$x^{2}y\times 3+5y\times 4-5x\times 2x=10xy$$

20 hosil qilish uchun 5 va 4 ni ko'paytirish.

$$x^{2}y\times 3+20y-5x\times 2x=10xy$$

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

$$x^{2}y\times 3+20y-5x^{2}\times 2=10xy$$

10 hosil qilish uchun 5 va 2 ni ko'paytirish.

$$x^{2}y\times 3+20y-10x^{2}=10xy$$

Ikkala tarafdan 10xy ni ayirish.

$$x^{2}y\times 3+20y-10x^{2}-10xy=0$$

10x^{2} ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$x^{2}y\times 3+20y-10xy=10x^{2}$$

y'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(x^{2}\times 3+20-10x\right)y=10x^{2}$$

Tenglama standart shaklda.

$$\left(3x^{2}-10x+20\right)y=10x^{2}$$

Ikki tarafini 3x^{2}-10x+20 ga bo‘ling.

$$\frac{\left(3x^{2}-10x+20\right)y}{3x^{2}-10x+20}=\frac{10x^{2}}{3x^{2}-10x+20}$$

3x^{2}-10x+20 ga bo'lish 3x^{2}-10x+20 ga ko'paytirishni bekor qiladi.

$$y=\frac{10x^{2}}{3x^{2}-10x+20}$$

y qiymati 0 teng bo‘lmaydi.

$$y=\frac{10x^{2}}{3x^{2}-10x+20}\text{, }y\neq 0$$

y uchun yechish

$$y=-\frac{10x^{2}}{-3x^{2}+10x-20}$$

$$x\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

y qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 5xy ga, 5,x,y ning eng kichik karralisiga ko‘paytiring.

$$xy\times 3x+5y\times 4-5x\times 2x=10xy$$

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

$$x^{2}y\times 3+5y\times 4-5x\times 2x=10xy$$

20 hosil qilish uchun 5 va 4 ni ko'paytirish.

$$x^{2}y\times 3+20y-5x\times 2x=10xy$$

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

$$x^{2}y\times 3+20y-5x^{2}\times 2=10xy$$

10 hosil qilish uchun 5 va 2 ni ko'paytirish.

$$x^{2}y\times 3+20y-10x^{2}=10xy$$

Ikkala tarafdan 10xy ni ayirish.

$$x^{2}y\times 3+20y-10x^{2}-10xy=0$$

10x^{2} ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$x^{2}y\times 3+20y-10xy=10x^{2}$$

y'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(x^{2}\times 3+20-10x\right)y=10x^{2}$$

Tenglama standart shaklda.

$$\left(3x^{2}-10x+20\right)y=10x^{2}$$

Ikki tarafini 3x^{2}-10x+20 ga bo‘ling.

$$\frac{\left(3x^{2}-10x+20\right)y}{3x^{2}-10x+20}=\frac{10x^{2}}{3x^{2}-10x+20}$$

3x^{2}-10x+20 ga bo'lish 3x^{2}-10x+20 ga ko'paytirishni bekor qiladi.

$$y=\frac{10x^{2}}{3x^{2}-10x+20}$$

y qiymati 0 teng bo‘lmaydi.

$$y=\frac{10x^{2}}{3x^{2}-10x+20}\text{, }y\neq 0$$

x uchun yechish (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{5}\left(\sqrt{y\left(40-7y\right)}+\sqrt{5}y\right)}{3y-10}\text{; }x=\frac{\sqrt{5}\left(-\sqrt{y\left(40-7y\right)}+\sqrt{5}y\right)}{3y-10}\text{, }&y\neq \frac{10}{3}\text{ and }y\neq 0\\x=2\text{, }&y=\frac{10}{3}\end{matrix}\right,$$

x uchun yechish

$$\left\{\begin{matrix}x=\frac{\sqrt{5y}\left(\sqrt{40-7y}+\sqrt{5y}\right)}{3y-10}\text{; }x=\frac{\sqrt{5y}\left(-\sqrt{40-7y}+\sqrt{5y}\right)}{3y-10}\text{, }&y\neq \frac{10}{3}\text{ and }y\leq \frac{40}{7}\text{ and }y>0\\x=2\text{, }&y=\frac{10}{3}\end{matrix}\right,$$