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

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

Solve for a (complex solution)

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

Steps for Solving Linear Equation

Add b to both sides.

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

Combine all terms containing a.

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

The equation is in standard form.

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

Divide both sides by b^{2}x^{2}-1.

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

Dividing by b^{2}x^{2}-1 undoes the multiplication by b^{2}x^{2}-1.

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

Divide b\left(1+xb\right) by b^{2}x^{2}-1.

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

Solve for a

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

Steps for Solving Linear Equation

Add b to both sides.

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

Combine all terms containing a.

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

The equation is in standard form.

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

Divide both sides by b^{2}x^{2}-1.

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

Dividing by b^{2}x^{2}-1 undoes the multiplication by b^{2}x^{2}-1.

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

Divide b\left(1+xb\right) by b^{2}x^{2}-1.

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

Solve for b

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