Solve x=L/A+L/B-x

$$x = \frac { L } { A } + \frac { L } { B } - x$$

Solve for A

$$\left\{\begin{matrix}A=-\frac{BL}{L-2Bx}\text{, }&B\neq 0\text{ and }L\neq 0\text{ and }x\neq \frac{L}{2B}\text{ and }L\neq 2Bx\\A\neq 0\text{, }&L=0\text{ and }x=0\text{ and }B\neq 0\end{matrix}\right.$$

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 AB, the least common multiple of A,B.

$$xAB=BL+AL-xAB$$

Subtract AL from both sides.

$$xAB-AL=BL-xAB$$

Add xAB to both sides.

$$xAB-AL+xAB=BL$$

Combine xAB and xAB to get 2xAB.

$$2xAB-AL=BL$$

Combine all terms containing A.

$$\left(2xB-L\right)A=BL$$

The equation is in standard form.

$$\left(2Bx-L\right)A=BL$$

Divide both sides by 2xB-L.

$$\frac{\left(2Bx-L\right)A}{2Bx-L}=\frac{BL}{2Bx-L}$$

Dividing by 2xB-L undoes the multiplication by 2xB-L.

$$A=\frac{BL}{2Bx-L}$$

Variable A cannot be equal to 0.

$$A=\frac{BL}{2Bx-L}\text{, }A\neq 0$$

Solve for B

$$\left\{\begin{matrix}B=-\frac{AL}{L-2Ax}\text{, }&A\neq 0\text{ and }L\neq 0\text{ and }x\neq \frac{L}{2A}\text{ and }L\neq 2Ax\\B\neq 0\text{, }&L=0\text{ and }x=0\text{ and }A\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable B cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by AB, the least common multiple of A,B.

$$xAB=BL+AL-xAB$$

Subtract BL from both sides.

$$xAB-BL=AL-xAB$$

Add xAB to both sides.

$$xAB-BL+xAB=AL$$

Combine xAB and xAB to get 2xAB.

$$2xAB-BL=AL$$

Combine all terms containing B.

$$\left(2xA-L\right)B=AL$$

The equation is in standard form.

$$\left(2Ax-L\right)B=AL$$

Divide both sides by 2xA-L.

$$\frac{\left(2Ax-L\right)B}{2Ax-L}=\frac{AL}{2Ax-L}$$

Dividing by 2xA-L undoes the multiplication by 2xA-L.

$$B=\frac{AL}{2Ax-L}$$

Variable B cannot be equal to 0.

$$B=\frac{AL}{2Ax-L}\text{, }B\neq 0$$