Solve a/x-1+1/x=1

$$\frac { a } { x - 1 } + \frac { 1 } { x } = 1$$

Solve for a

$$a=\frac{\left(x-1\right)^{2}}{x}$$

$$x\neq 1\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x\left(x-1\right), the least common multiple of x-1,x.

$$xa+x-1=x\left(x-1\right)$$

Use the distributive property to multiply x by x-1.

$$xa+x-1=x^{2}-x$$

Subtract x from both sides.

$$xa-1=x^{2}-x-x$$

Combine -x and -x to get -2x.

$$xa-1=x^{2}-2x$$

Add 1 to both sides.

$$xa=x^{2}-2x+1$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{\left(x-1\right)^{2}}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{\left(x-1\right)^{2}}{x}$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{a\left(a+4\right)}+a+2}{2}$$

$$x=\frac{\sqrt{a\left(a+4\right)}+a+2}{2}\text{, }a\neq 0$$

Solve for x

$$x=\frac{-\sqrt{a\left(a+4\right)}+a+2}{2}$$

$$x=\frac{\sqrt{a\left(a+4\right)}+a+2}{2}\text{, }a\leq -4\text{ or }a>0$$