Solve 1/2x-1/x=1/2b

$$\frac { 1 } { 2 } x - \frac { 1 } { x } = \frac { 1 } { 2 } b$$

Solve for b

$$b=x-\frac{2}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$\frac{1}{2}x\times 2x-2=\frac{1}{2}b\times 2x$$

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

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

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

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

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

$$x^{2}-2=bx$$

Swap sides so that all variable terms are on the left hand side.

$$bx=x^{2}-2$$

The equation is in standard form.

$$xb=x^{2}-2$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{x^{2}-2}{x}$$

Dividing by x undoes the multiplication by x.

$$b=\frac{x^{2}-2}{x}$$

Divide x^{2}-2 by x.

$$b=x-\frac{2}{x}$$

Solve for x

$$x=\frac{\sqrt{b^{2}+8}+b}{2}$$

$$x=\frac{-\sqrt{b^{2}+8}+b}{2}$$