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

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

Solve for N

$$N=\frac{x-3}{2}$$

$$x\neq 1$$

Steps for Solving Linear Equation

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

$$x-1=\left(N+1\right)\times 2$$

Use the distributive property to multiply N+1 by 2.

$$x-1=2N+2$$

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

$$2N+2=x-1$$

Subtract 2 from both sides.

$$2N=x-1-2$$

Subtract 2 from -1 to get -3.

$$2N=x-3$$

Divide both sides by 2.

$$\frac{2N}{2}=\frac{x-3}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$N=\frac{x-3}{2}$$

Variable N cannot be equal to -1.

$$N=\frac{x-3}{2}\text{, }N\neq -1$$

Solve for x

$$x=2N+3$$

$$N\neq -1$$

Solution Steps

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

$$x-1=\left(N+1\right)\times 2$$

Use the distributive property to multiply N+1 by 2.

$$x-1=2N+2$$

Add 1 to both sides.

$$x=2N+2+1$$

Add 2 and 1 to get 3.

$$x=2N+3$$

Variable x cannot be equal to 1.

$$x=2N+3\text{, }x\neq 1$$