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

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

Solve for n

$$\left\{\begin{matrix}n=-\frac{\left(x-2\right)\left(y-1\right)}{x-1}\text{, }&y\neq 1\text{ and }x\neq 2\text{ and }x\neq 1\\n\neq 0\text{, }&y=1\text{ and }x=1\end{matrix}\right.$$

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 n\left(x-2\right), the least common multiple of x-2,n.

$$n\left(x-1\right)=\left(x-2\right)\left(1-y\right)$$

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

$$nx-n=\left(x-2\right)\left(1-y\right)$$

Use the distributive property to multiply x-2 by 1-y.

$$nx-n=x-xy-2+2y$$

Combine all terms containing n.

$$\left(x-1\right)n=x-xy-2+2y$$

The equation is in standard form.

$$\left(x-1\right)n=-xy+x+2y-2$$

Divide both sides by x-1.

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

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

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

Variable n cannot be equal to 0.

$$n=\frac{\left(1-y\right)\left(x-2\right)}{x-1}\text{, }n\neq 0$$

Solve for x

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

$$n\neq 0\text{ and }y\neq 1-n$$

Steps for Solving Linear Equation

Variable x cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by n\left(x-2\right), the least common multiple of x-2,n.

$$n\left(x-1\right)=\left(x-2\right)\left(1-y\right)$$

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

$$nx-n=\left(x-2\right)\left(1-y\right)$$

Use the distributive property to multiply x-2 by 1-y.

$$nx-n=x-xy-2+2y$$

Subtract x from both sides.

$$nx-n-x=-xy-2+2y$$

Add xy to both sides.

$$nx-n-x+xy=-2+2y$$

Add n to both sides.

$$nx-x+xy=-2+2y+n$$

Combine all terms containing x.

$$\left(n-1+y\right)x=-2+2y+n$$

The equation is in standard form.

$$\left(y+n-1\right)x=2y+n-2$$

Divide both sides by n-1+y.

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

Dividing by n-1+y undoes the multiplication by n-1+y.

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

Variable x cannot be equal to 2.

$$x=\frac{2y+n-2}{y+n-1}\text{, }x\neq 2$$