Solve k=xd-kx/x+m

$$k = \frac { x d - k x } { x + m }$$

Solve for d (complex solution)

$$\left\{\begin{matrix}d=\frac{k\left(2x+m\right)}{x}\text{, }&x\neq 0\text{ and }x\neq -m\\d\in \mathrm{C}\text{, }&k=0\text{ and }x=0\text{ and }m\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x+m.

$$k\left(x+m\right)=xd-kx$$

Use the distributive property to multiply k by x+m.

$$kx+km=xd-kx$$

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

$$xd-kx=kx+km$$

Add kx to both sides.

$$xd=kx+km+kx$$

Combine kx and kx to get 2kx.

$$xd=2kx+km$$

Divide both sides by x.

$$\frac{xd}{x}=\frac{k\left(2x+m\right)}{x}$$

Dividing by x undoes the multiplication by x.

$$d=\frac{k\left(2x+m\right)}{x}$$

Solve for k (complex solution)

$$\left\{\begin{matrix}k=\frac{dx}{2x+m}\text{, }&x\neq -\frac{m}{2}\text{ and }x\neq -m\\k\in \mathrm{C}\text{, }&d=0\text{ and }x=-\frac{m}{2}\text{ and }m\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract \frac{xd-kx}{x+m} from both sides.

$$k-\frac{xd-kx}{x+m}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply k times \frac{x+m}{x+m}.

$$\frac{k\left(x+m\right)}{x+m}-\frac{xd-kx}{x+m}=0$$

Since \frac{k\left(x+m\right)}{x+m} and \frac{xd-kx}{x+m} have the same denominator, subtract them by subtracting their numerators.

$$\frac{k\left(x+m\right)-\left(xd-kx\right)}{x+m}=0$$

Do the multiplications in k\left(x+m\right)-\left(xd-kx\right).

$$\frac{kx+km-xd+xk}{x+m}=0$$

Combine like terms in kx+km-xd+xk.

$$\frac{2kx+km-xd}{x+m}=0$$

Multiply both sides of the equation by x+m.

$$2kx+km-xd=0$$

Add xd to both sides. Anything plus zero gives itself.

$$2kx+km=xd$$

Combine all terms containing k.

$$\left(2x+m\right)k=xd$$

The equation is in standard form.

$$\left(2x+m\right)k=dx$$

Divide both sides by m+2x.

$$\frac{\left(2x+m\right)k}{2x+m}=\frac{dx}{2x+m}$$

Dividing by m+2x undoes the multiplication by m+2x.

$$k=\frac{dx}{2x+m}$$

Solve for d

$$\left\{\begin{matrix}d=\frac{k\left(2x+m\right)}{x}\text{, }&x\neq 0\text{ and }x\neq -m\\d\in \mathrm{R}\text{, }&k=0\text{ and }x=0\text{ and }m\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x+m.

$$k\left(x+m\right)=xd-kx$$

Use the distributive property to multiply k by x+m.

$$kx+km=xd-kx$$

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

$$xd-kx=kx+km$$

Add kx to both sides.

$$xd=kx+km+kx$$

Combine kx and kx to get 2kx.

$$xd=2kx+km$$

Divide both sides by x.

$$\frac{xd}{x}=\frac{k\left(2x+m\right)}{x}$$

Dividing by x undoes the multiplication by x.

$$d=\frac{k\left(2x+m\right)}{x}$$

Solve for k

$$\left\{\begin{matrix}k=\frac{dx}{2x+m}\text{, }&x\neq -\frac{m}{2}\text{ and }x\neq -m\\k\in \mathrm{R}\text{, }&d=0\text{ and }x=-\frac{m}{2}\text{ and }m\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract \frac{xd-kx}{x+m} from both sides.

$$k-\frac{xd-kx}{x+m}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply k times \frac{x+m}{x+m}.

$$\frac{k\left(x+m\right)}{x+m}-\frac{xd-kx}{x+m}=0$$

Since \frac{k\left(x+m\right)}{x+m} and \frac{xd-kx}{x+m} have the same denominator, subtract them by subtracting their numerators.

$$\frac{k\left(x+m\right)-\left(xd-kx\right)}{x+m}=0$$

Do the multiplications in k\left(x+m\right)-\left(xd-kx\right).

$$\frac{kx+km-xd+xk}{x+m}=0$$

Combine like terms in kx+km-xd+xk.

$$\frac{2kx+km-xd}{x+m}=0$$

Multiply both sides of the equation by x+m.

$$2kx+km-xd=0$$

Add xd to both sides. Anything plus zero gives itself.

$$2kx+km=xd$$

Combine all terms containing k.

$$\left(2x+m\right)k=xd$$

The equation is in standard form.

$$\left(2x+m\right)k=dx$$

Divide both sides by m+2x.

$$\frac{\left(2x+m\right)k}{2x+m}=\frac{dx}{2x+m}$$

Dividing by m+2x undoes the multiplication by m+2x.

$$k=\frac{dx}{2x+m}$$