Solve x/alpha+x/4=1

$$\frac { x } { \alpha } + \frac { x } { 4 } = 1$$

Solve for x

$$x=\frac{4\alpha }{\alpha +4}$$

$$\alpha \neq -4\text{ and }\alpha \neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4\alpha , the least common multiple of \alpha ,4.

$$4x+\alpha x=4\alpha$$

Combine all terms containing x.

$$\left(4+\alpha \right)x=4\alpha$$

The equation is in standard form.

$$\left(\alpha +4\right)x=4\alpha$$

Divide both sides by \alpha +4.

$$\frac{\left(\alpha +4\right)x}{\alpha +4}=\frac{4\alpha }{\alpha +4}$$

Dividing by \alpha +4 undoes the multiplication by \alpha +4.

$$x=\frac{4\alpha }{\alpha +4}$$

Solve for α

$$\alpha =-\frac{4x}{x-4}$$

$$x\neq 0\text{ and }x\neq 4$$

Steps for Solving Linear Equation

Variable \alpha cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4\alpha , the least common multiple of \alpha ,4.

$$4x+\alpha x=4\alpha$$

Subtract 4\alpha from both sides.

$$4x+\alpha x-4\alpha =0$$

Subtract 4x from both sides. Anything subtracted from zero gives its negation.

$$\alpha x-4\alpha =-4x$$

Combine all terms containing \alpha .

$$\left(x-4\right)\alpha =-4x$$

Divide both sides by x-4.

$$\frac{\left(x-4\right)\alpha }{x-4}=-\frac{4x}{x-4}$$

Dividing by x-4 undoes the multiplication by x-4.

$$\alpha =-\frac{4x}{x-4}$$

Variable \alpha cannot be equal to 0.

$$\alpha =-\frac{4x}{x-4}\text{, }\alpha \neq 0$$