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

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

Solve for x

$$x=-\frac{4}{y-1}$$

$$y\neq -3\text{ and }y\neq 1$$

Steps for Solving Linear Equation

Variable x cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by x-1, the least common multiple of x-1,1-x.

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

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

$$yx+2-x+1=-1$$

Add 2 and 1 to get 3.

$$yx+3-x=-1$$

Subtract 3 from both sides.

$$yx-x=-1-3$$

Subtract 3 from -1 to get -4.

$$yx-x=-4$$

Combine all terms containing x.

$$\left(y-1\right)x=-4$$

Divide both sides by y-1.

$$\frac{\left(y-1\right)x}{y-1}=-\frac{4}{y-1}$$

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

$$x=-\frac{4}{y-1}$$

Variable x cannot be equal to 1.

$$x=-\frac{4}{y-1}\text{, }x\neq 1$$

Solve for y

$$y=\frac{x-4}{x}$$

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

Steps for Solving Linear Equation

Multiply both sides of the equation by x-1, the least common multiple of x-1,1-x.

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

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

$$yx+2-x+1=-1$$

Add 2 and 1 to get 3.

$$yx+3-x=-1$$

Subtract 3 from both sides.

$$yx-x=-1-3$$

Subtract 3 from -1 to get -4.

$$yx-x=-4$$

Add x to both sides.

$$yx=-4+x$$

The equation is in standard form.

$$xy=x-4$$

Divide both sides by x.

$$\frac{xy}{x}=\frac{x-4}{x}$$

Dividing by x undoes the multiplication by x.

$$y=\frac{x-4}{x}$$