Solve 1/n=1/y-1/2

$$\frac { 1 } { n } = \frac { 1 } { y } - \frac { 1 } { 2 }$$

Solve for n

$$n=-\frac{2y}{y-2}$$

$$y\neq 0\text{ and }y\neq 2$$

Steps for Solving Linear Equation

Variable n cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2ny, the least common multiple of n,y,2.

$$2y=2n+2ny\left(-\frac{1}{2}\right)$$

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

$$2y=2n-ny$$

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

$$2n-ny=2y$$

Combine all terms containing n.

$$\left(2-y\right)n=2y$$

Divide both sides by 2-y.

$$\frac{\left(2-y\right)n}{2-y}=\frac{2y}{2-y}$$

Dividing by 2-y undoes the multiplication by 2-y.

$$n=\frac{2y}{2-y}$$

Variable n cannot be equal to 0.

$$n=\frac{2y}{2-y}\text{, }n\neq 0$$

Solve for y

$$y=\frac{2n}{n+2}$$

$$n\neq 0\text{ and }n\neq -2$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2ny, the least common multiple of n,y,2.

$$2y=2n+2ny\left(-\frac{1}{2}\right)$$

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

$$2y=2n-ny$$

Add ny to both sides.

$$2y+ny=2n$$

Combine all terms containing y.

$$\left(2+n\right)y=2n$$

The equation is in standard form.

$$\left(n+2\right)y=2n$$

Divide both sides by 2+n.

$$\frac{\left(n+2\right)y}{n+2}=\frac{2n}{n+2}$$

Dividing by 2+n undoes the multiplication by 2+n.

$$y=\frac{2n}{n+2}$$

Variable y cannot be equal to 0.

$$y=\frac{2n}{n+2}\text{, }y\neq 0$$