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

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

Solve for a (complex solution)

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

Steps for Solving Linear Equation

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

$$2\left(x-a\right)=2xx-2a\times 2x+2x\times \frac{1}{2}$$

Use the distributive property to multiply 2 by x-a.

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

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

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

Multiply -2 and 2 to get -4.

$$2x-2a=2x^{2}-4ax+2x\times \frac{1}{2}$$

Multiply 2 and \frac{1}{2} to get 1.

$$2x-2a=2x^{2}-4ax+x$$

Add 4ax to both sides.

$$2x-2a+4ax=2x^{2}+x$$

Subtract 2x from both sides.

$$-2a+4ax=2x^{2}+x-2x$$

Combine x and -2x to get -x.

$$-2a+4ax=2x^{2}-x$$

Combine all terms containing a.

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

The equation is in standard form.

$$\left(4x-2\right)a=2x^{2}-x$$

Divide both sides by -2+4x.

$$\frac{\left(4x-2\right)a}{4x-2}=\frac{x\left(2x-1\right)}{4x-2}$$

Dividing by -2+4x undoes the multiplication by -2+4x.

$$a=\frac{x\left(2x-1\right)}{4x-2}$$

Divide x\left(-1+2x\right) by -2+4x.

$$a=\frac{x}{2}$$

Solve for a

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

Steps for Solving Linear Equation

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

$$2\left(x-a\right)=2xx-2a\times 2x+2x\times \frac{1}{2}$$

Use the distributive property to multiply 2 by x-a.

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

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

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

Multiply -2 and 2 to get -4.

$$2x-2a=2x^{2}-4ax+2x\times \frac{1}{2}$$

Multiply 2 and \frac{1}{2} to get 1.

$$2x-2a=2x^{2}-4ax+x$$

Add 4ax to both sides.

$$2x-2a+4ax=2x^{2}+x$$

Subtract 2x from both sides.

$$-2a+4ax=2x^{2}+x-2x$$

Combine x and -2x to get -x.

$$-2a+4ax=2x^{2}-x$$

Combine all terms containing a.

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

The equation is in standard form.

$$\left(4x-2\right)a=2x^{2}-x$$

Divide both sides by -2+4x.

$$\frac{\left(4x-2\right)a}{4x-2}=\frac{x\left(2x-1\right)}{4x-2}$$

Dividing by -2+4x undoes the multiplication by -2+4x.

$$a=\frac{x\left(2x-1\right)}{4x-2}$$

Divide x\left(-1+2x\right) by -2+4x.

$$a=\frac{x}{2}$$

Solve for x

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