Solve x+m/x=c+m/c

$$x + \frac { m } { x } = c + \frac { m } { c }$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=cx\text{, }&x\neq 0\text{ and }c\neq 0\\m\in \mathrm{C}\text{, }&x=c\text{ and }c\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by cx, the least common multiple of x,c.

$$cxx+cm=cxc+xm$$

Multiply x and x to get x^{2}.

$$cx^{2}+cm=cxc+xm$$

Multiply c and c to get c^{2}.

$$cx^{2}+cm=c^{2}x+xm$$

Subtract xm from both sides.

$$cx^{2}+cm-xm=c^{2}x$$

Subtract cx^{2} from both sides.

$$cm-xm=c^{2}x-cx^{2}$$

Reorder the terms.

$$-mx+cm=-cx^{2}+xc^{2}$$

Combine all terms containing m.

$$\left(-x+c\right)m=-cx^{2}+xc^{2}$$

The equation is in standard form.

$$\left(c-x\right)m=xc^{2}-cx^{2}$$

Divide both sides by c-x.

$$\frac{\left(c-x\right)m}{c-x}=\frac{cx\left(c-x\right)}{c-x}$$

Dividing by c-x undoes the multiplication by c-x.

$$m=\frac{cx\left(c-x\right)}{c-x}$$

Divide xc\left(-x+c\right) by c-x.

$$m=cx$$

Solve for m

$$\left\{\begin{matrix}m=cx\text{, }&x\neq 0\text{ and }c\neq 0\\m\in \mathrm{R}\text{, }&x=c\text{ and }c\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by cx, the least common multiple of x,c.

$$cxx+cm=cxc+xm$$

Multiply x and x to get x^{2}.

$$cx^{2}+cm=cxc+xm$$

Multiply c and c to get c^{2}.

$$cx^{2}+cm=c^{2}x+xm$$

Subtract xm from both sides.

$$cx^{2}+cm-xm=c^{2}x$$

Subtract cx^{2} from both sides.

$$cm-xm=c^{2}x-cx^{2}$$

Reorder the terms.

$$-mx+cm=-cx^{2}+xc^{2}$$

Combine all terms containing m.

$$\left(-x+c\right)m=-cx^{2}+xc^{2}$$

The equation is in standard form.

$$\left(c-x\right)m=xc^{2}-cx^{2}$$

Divide both sides by c-x.

$$\frac{\left(c-x\right)m}{c-x}=\frac{cx\left(c-x\right)}{c-x}$$

Dividing by c-x undoes the multiplication by c-x.

$$m=\frac{cx\left(c-x\right)}{c-x}$$

Divide xc\left(-x+c\right) by c-x.

$$m=cx$$

Solve for c

$$\left\{\begin{matrix}c=x\text{, }&x\neq 0\\c=\frac{m}{x}\text{, }&x\neq 0\text{ and }m\neq 0\end{matrix}\right.$$