Solve A+x=r*x/t

$$A + x = \frac { r \cdot x } { t }$$

Solve for A

$$A=\frac{x\left(r-t\right)}{t}$$

$$t\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by t.

$$tA+tx=rx$$

Subtract tx from both sides.

$$tA=rx-tx$$

Divide both sides by t.

$$\frac{tA}{t}=\frac{x\left(r-t\right)}{t}$$

Dividing by t undoes the multiplication by t.

$$A=\frac{x\left(r-t\right)}{t}$$

Solve for r

$$\left\{\begin{matrix}r=\frac{t\left(x+A\right)}{x}\text{, }&x\neq 0\text{ and }t\neq 0\\r\in \mathrm{R}\text{, }&A=0\text{ and }x=0\text{ and }t\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by t.

$$tA+tx=rx$$

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

$$rx=tA+tx$$

The equation is in standard form.

$$xr=tx+At$$

Divide both sides by x.

$$\frac{xr}{x}=\frac{t\left(x+A\right)}{x}$$

Dividing by x undoes the multiplication by x.

$$r=\frac{t\left(x+A\right)}{x}$$