Solve bx/a=x^2+1

$$\frac { b x } { a } = x ^ { 2 } + 1$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{bx}{x^{2}+1}\text{, }&x\neq 0\text{ and }b\neq 0\text{ and }x\neq i\text{ and }x\neq -i\\a\neq 0\text{, }&\left(x=-i\text{ or }x=i\right)\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by a.

$$bx=ax^{2}+a$$

Swap sides so that all variable terms are on the left hand side.

$$ax^{2}+a=bx$$

Combine all terms containing a.

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

Divide both sides by x^{2}+1.

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

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

$$a=\frac{bx}{x^{2}+1}$$

Variable a cannot be equal to 0.

$$a=\frac{bx}{x^{2}+1}\text{, }a\neq 0$$

Solve for a

$$a=\frac{bx}{x^{2}+1}$$

$$x\neq 0\text{ and }b\neq 0$$

Steps for Solving Linear Equation

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by a.

$$bx=ax^{2}+a$$

Swap sides so that all variable terms are on the left hand side.

$$ax^{2}+a=bx$$

Combine all terms containing a.

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

Divide both sides by x^{2}+1.

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

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

$$a=\frac{bx}{x^{2}+1}$$

Variable a cannot be equal to 0.

$$a=\frac{bx}{x^{2}+1}\text{, }a\neq 0$$

Solve for b

$$b=ax+\frac{a}{x}$$

$$x\neq 0\text{ and }a\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by a.

$$bx=ax^{2}+a$$

The equation is in standard form.

$$xb=ax^{2}+a$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{ax^{2}+a}{x}$$

Dividing by x undoes the multiplication by x.

$$b=\frac{ax^{2}+a}{x}$$

Divide ax^{2}+a by x.

$$b=ax+\frac{a}{x}$$