Solve x/x+1=1/an

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

Solve for a

$$\left\{\begin{matrix}a=n+\frac{n}{x}\text{, }&x\neq -1\text{ and }n\neq 0\text{ and }x\neq 0\\a\neq 0\text{, }&n=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by a\left(x+1\right), the least common multiple of x+1,a.

$$ax=\left(x+1\right)\times 1n$$

Use the distributive property to multiply x+1 by 1.

$$ax=\left(x+1\right)n$$

Use the distributive property to multiply x+1 by n.

$$ax=xn+n$$

The equation is in standard form.

$$xa=nx+n$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{nx+n}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{nx+n}{x}$$

Divide nx+n by x.

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

Variable a cannot be equal to 0.

$$a=n+\frac{n}{x}\text{, }a\neq 0$$

Solve for n

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

$$x\neq -1\text{ and }a\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by a\left(x+1\right), the least common multiple of x+1,a.

$$ax=\left(x+1\right)\times 1n$$

Use the distributive property to multiply x+1 by 1.

$$ax=\left(x+1\right)n$$

Use the distributive property to multiply x+1 by n.

$$ax=xn+n$$

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

$$xn+n=ax$$

Combine all terms containing n.

$$\left(x+1\right)n=ax$$

Divide both sides by x+1.

$$\frac{\left(x+1\right)n}{x+1}=\frac{ax}{x+1}$$

Dividing by x+1 undoes the multiplication by x+1.

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