Solve -a/x^2-a/x+1=0

$$- \frac{ a }{ { x }^{ 2 } } - \frac{ a }{ x } +1=0$$

Solve for a

$$a=\frac{x^{2}}{x+1}$$

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

Steps for Solving Linear Equation

Multiply both sides of the equation by x^{2}, the least common multiple of x^{2},x.

$$-a-xa+x^{2}=0$$

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

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

Reorder the terms.

$$-ax-a=-x^{2}$$

Combine all terms containing a.

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

Divide both sides by -1-x.

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

Dividing by -1-x undoes the multiplication by -1-x.

$$a=-\frac{x^{2}}{-x-1}$$

Divide -x^{2} by -1-x.

$$a=\frac{x^{2}}{x+1}$$

Solve for x (complex solution)

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

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

Solve for x

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

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