x^2+4x+3edivhx=x+1 eching

$${ x }^{ 2 } +4x+3e \div hx = x+1$$

h uchun yechish

$$h=-\frac{3ex}{x^{2}+3x-1}$$

$$x\neq 0\text{ and }x\neq \frac{\sqrt{13}-3}{2}\text{ and }x\neq \frac{-\sqrt{13}-3}{2}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

h qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini h ga ko'paytirish.

$$hx^{2}+4xh+3ex=hx+h$$

Ikkala tarafdan hx ni ayirish.

$$hx^{2}+4xh+3ex-hx=h$$

3xh ni olish uchun 4xh va -hx ni birlashtirish.

$$hx^{2}+3xh+3ex=h$$

Ikkala tarafdan h ni ayirish.

$$hx^{2}+3xh+3ex-h=0$$

Ikkala tarafdan 3ex ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$hx^{2}+3xh-h=-3ex$$

h'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(x^{2}+3x-1\right)h=-3ex$$

Ikki tarafini x^{2}+3x-1 ga bo‘ling.

$$\frac{\left(x^{2}+3x-1\right)h}{x^{2}+3x-1}=-\frac{3ex}{x^{2}+3x-1}$$

x^{2}+3x-1 ga bo'lish x^{2}+3x-1 ga ko'paytirishni bekor qiladi.

$$h=-\frac{3ex}{x^{2}+3x-1}$$

h qiymati 0 teng bo‘lmaydi.

$$h=-\frac{3ex}{x^{2}+3x-1}\text{, }h\neq 0$$

x uchun yechish

$$x=\frac{\sqrt{13h^{2}+18eh+9e^{2}}-3h-3e}{2h}$$

$$x=-\frac{\sqrt{13h^{2}+18eh+9e^{2}}+3h+3e}{2h}\text{, }h\neq 0$$