30x*(y+20-x)/(3x+5)y(20-x)=6*(x+5)/3x+5 eching

$$\frac{ 30x \times (y+20-x) }{ (3x+5)y(20-x) } = \frac{ 6 \times (x+5) }{ 3x+5 }$$

y uchun yechish

$$y=-\frac{5x\left(20-x\right)}{x^{2}-10x-100}$$

$$x\neq 20\text{ and }x\neq 0\text{ and }x\neq 5\sqrt{5}+5\text{ and }x\neq 5-5\sqrt{5}\text{ and }x\neq -\frac{5}{3}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

y qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini y\left(x-20\right)\left(3x+5\right) ga, \left(3x+5\right)y\left(20-x\right),3x+5 ning eng kichik karralisiga ko‘paytiring.

$$-30x\left(y+20-x\right)=y\left(x-20\right)\times 6\left(x+5\right)$$

-30x ga y+20-x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-30xy-600x+30x^{2}=y\left(x-20\right)\times 6\left(x+5\right)$$

y ga x-20 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-30xy-600x+30x^{2}=\left(yx-20y\right)\times 6\left(x+5\right)$$

yx-20y ga 6 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-30xy-600x+30x^{2}=\left(6yx-120y\right)\left(x+5\right)$$

6yx-120y ga x+5 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$-30xy-600x+30x^{2}=6yx^{2}-90yx-600y$$

Ikkala tarafdan 6yx^{2} ni ayirish.

$$-30xy-600x+30x^{2}-6yx^{2}=-90yx-600y$$

90yx ni ikki tarafga qo’shing.

$$-30xy-600x+30x^{2}-6yx^{2}+90yx=-600y$$

600y ni ikki tarafga qo’shing.

$$-30xy-600x+30x^{2}-6yx^{2}+90yx+600y=0$$

60xy ni olish uchun -30xy va 90yx ni birlashtirish.

$$60xy-600x+30x^{2}-6yx^{2}+600y=0$$

600x ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$60xy+30x^{2}-6yx^{2}+600y=600x$$

Ikkala tarafdan 30x^{2} ni ayirish.

$$60xy-6yx^{2}+600y=600x-30x^{2}$$

y'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(60x-6x^{2}+600\right)y=600x-30x^{2}$$

Tenglama standart shaklda.

$$\left(600+60x-6x^{2}\right)y=600x-30x^{2}$$

Ikki tarafini 60x-6x^{2}+600 ga bo‘ling.

$$\frac{\left(600+60x-6x^{2}\right)y}{600+60x-6x^{2}}=\frac{30x\left(20-x\right)}{600+60x-6x^{2}}$$

60x-6x^{2}+600 ga bo'lish 60x-6x^{2}+600 ga ko'paytirishni bekor qiladi.

$$y=\frac{30x\left(20-x\right)}{600+60x-6x^{2}}$$

30x\left(20-x\right) ni 60x-6x^{2}+600 ga bo'lish.

$$y=\frac{5x\left(20-x\right)}{100+10x-x^{2}}$$

y qiymati 0 teng bo‘lmaydi.

$$y=\frac{5x\left(20-x\right)}{100+10x-x^{2}}\text{, }y\neq 0$$

x uchun yechish

$$\left\{\begin{matrix}x=\frac{5\left(-\sqrt{5\left(y^{2}-8y+20\right)}+y-10\right)}{y-5}\text{, }&y\neq 0\text{ and }y\neq 5\\x=\frac{5\left(\sqrt{5\left(y^{2}-8y+20\right)}+y-10\right)}{y-5}\text{, }&y\neq -\frac{65}{29}\text{ and }y\neq 5\text{ and }y\neq 0\\x=10\text{, }&y=5\end{matrix}\right,$$