Solve 1/x+1/n=n/n+n

$$\frac { 1 } { x } + \frac { 1 } { n } = \frac { n } { n + n }$$

Solve for n

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

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

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 2nx, the least common multiple of x,n,n+n.

$$2n+2x=xn$$

Subtract xn from both sides.

$$2n+2x-xn=0$$

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

$$2n-xn=-2x$$

Combine all terms containing n.

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

Divide both sides by 2-x.

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

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

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

Variable n cannot be equal to 0.

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

Solve for x

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

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

Steps for Solving Linear Equation

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

$$2n+2x=xn$$

Subtract xn from both sides.

$$2n+2x-xn=0$$

Subtract 2n from both sides. Anything subtracted from zero gives its negation.

$$2x-xn=-2n$$

Combine all terms containing x.

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

Divide both sides by 2-n.

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

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

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

Variable x cannot be equal to 0.

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