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

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

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{1}{x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&x=\frac{1}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$1+2axx-ax+x\left(-2\right)=0$$

Multiply x and x to get x^{2}.

$$1+2ax^{2}-ax+x\left(-2\right)=0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

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

Subtract x\left(-2\right) from both sides.

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

Multiply -1 and -2 to get 2.

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

Combine all terms containing a.

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

The equation is in standard form.

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

Divide both sides by 2x^{2}-x.

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

Dividing by 2x^{2}-x undoes the multiplication by 2x^{2}-x.

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

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

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

Solve for a

$$\left\{\begin{matrix}a=\frac{1}{x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&x=\frac{1}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$1+2axx-ax+x\left(-2\right)=0$$

Multiply x and x to get x^{2}.

$$1+2ax^{2}-ax+x\left(-2\right)=0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

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

Subtract x\left(-2\right) from both sides.

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

Multiply -1 and -2 to get 2.

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

Combine all terms containing a.

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

The equation is in standard form.

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

Divide both sides by 2x^{2}-x.

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

Dividing by 2x^{2}-x undoes the multiplication by 2x^{2}-x.

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

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

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

Solve for x

$$\left\{\begin{matrix}\\x=\frac{1}{2}\text{, }&\text{unconditionally}\\x=\frac{1}{a}\text{, }&a\neq 0\end{matrix}\right.$$