ab^2x^2-b-a=b^2x eching

$$a b ^ { 2 } x ^ { 2 } - b - a = b ^ { 2 } x$$

a uchun yechish (complex solution)

$$\left\{\begin{matrix}a=\frac{b}{bx-1}\text{, }&x=0\text{ or }b\neq \frac{1}{x}\\a\in \mathrm{C}\text{, }&b=-\frac{1}{x}\text{ and }x\neq 0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

b ni ikki tarafga qo’shing.

$$ab^{2}x^{2}-a=b^{2}x+b$$

a'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(b^{2}x^{2}-1\right)a=b^{2}x+b$$

Tenglama standart shaklda.

$$\left(b^{2}x^{2}-1\right)a=xb^{2}+b$$

Ikki tarafini b^{2}x^{2}-1 ga bo‘ling.

$$\frac{\left(b^{2}x^{2}-1\right)a}{b^{2}x^{2}-1}=\frac{b\left(bx+1\right)}{b^{2}x^{2}-1}$$

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

$$a=\frac{b\left(bx+1\right)}{b^{2}x^{2}-1}$$

b\left(1+xb\right) ni b^{2}x^{2}-1 ga bo'lish.

$$a=\frac{b}{bx-1}$$

a uchun yechish

$$\left\{\begin{matrix}a=\frac{b}{bx-1}\text{, }&x=0\text{ or }b\neq \frac{1}{x}\\a\in \mathrm{R}\text{, }&b=-\frac{1}{x}\text{ and }x\neq 0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

b ni ikki tarafga qo’shing.

$$ab^{2}x^{2}-a=b^{2}x+b$$

a'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(b^{2}x^{2}-1\right)a=b^{2}x+b$$

Tenglama standart shaklda.

$$\left(b^{2}x^{2}-1\right)a=xb^{2}+b$$

Ikki tarafini b^{2}x^{2}-1 ga bo‘ling.

$$\frac{\left(b^{2}x^{2}-1\right)a}{b^{2}x^{2}-1}=\frac{b\left(bx+1\right)}{b^{2}x^{2}-1}$$

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

$$a=\frac{b\left(bx+1\right)}{b^{2}x^{2}-1}$$

b\left(1+xb\right) ni b^{2}x^{2}-1 ga bo'lish.

$$a=\frac{b}{bx-1}$$

b uchun yechish

$$\left\{\begin{matrix}b=-\frac{1}{x}\text{, }&x\neq 0\\b=\frac{a}{ax-1}\text{, }&x=0\text{ or }a\neq \frac{1}{x}\end{matrix}\right,$$