Solve 1/x-1+4/y+2=1

$$\frac { 1 } { x - 1 } + \frac { 4 } { y + 2 } = 1$$

Solve for x (complex solution)

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

$$y\neq -2\text{ and }y\neq 2$$

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 \left(x-1\right)\left(y+2\right), the least common multiple of x-1,y+2.

$$y+2+\left(x-1\right)\times 4=\left(x-1\right)\left(y+2\right)$$

Use the distributive property to multiply x-1 by 4.

$$y+2+4x-4=\left(x-1\right)\left(y+2\right)$$

Subtract 4 from 2 to get -2.

$$y-2+4x=\left(x-1\right)\left(y+2\right)$$

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

$$y-2+4x=xy+2x-y-2$$

Subtract xy from both sides.

$$y-2+4x-xy=2x-y-2$$

Subtract 2x from both sides.

$$y-2+4x-xy-2x=-y-2$$

Combine 4x and -2x to get 2x.

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

Subtract y from both sides.

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

Combine -y and -y to get -2y.

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

Add 2 to both sides.

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

Add -2 and 2 to get 0.

$$2x-xy=-2y$$

Combine all terms containing x.

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

Divide both sides by -y+2.

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

Dividing by -y+2 undoes the multiplication by -y+2.

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

Variable x cannot be equal to 1.

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

Solve for x

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

$$|y|\neq 2$$

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 \left(x-1\right)\left(y+2\right), the least common multiple of x-1,y+2.

$$y+2+\left(x-1\right)\times 4=\left(x-1\right)\left(y+2\right)$$

Use the distributive property to multiply x-1 by 4.

$$y+2+4x-4=\left(x-1\right)\left(y+2\right)$$

Subtract 4 from 2 to get -2.

$$y-2+4x=\left(x-1\right)\left(y+2\right)$$

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

$$y-2+4x=xy+2x-y-2$$

Subtract xy from both sides.

$$y-2+4x-xy=2x-y-2$$

Subtract 2x from both sides.

$$y-2+4x-xy-2x=-y-2$$

Combine 4x and -2x to get 2x.

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

Subtract y from both sides.

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

Combine -y and -y to get -2y.

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

Add 2 to both sides.

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

Add -2 and 2 to get 0.

$$2x-xy=-2y$$

Combine all terms containing x.

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

Divide both sides by -y+2.

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

Dividing by -y+2 undoes the multiplication by -y+2.

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

Variable x cannot be equal to 1.

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

Solve for y

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

$$x\neq 1\text{ and }x\neq 2$$

Steps for Solving Linear Equation

Variable y cannot be equal to -2 since division by zero is not defined. Multiply both sides of the equation by \left(x-1\right)\left(y+2\right), the least common multiple of x-1,y+2.

$$y+2+\left(x-1\right)\times 4=\left(x-1\right)\left(y+2\right)$$

Use the distributive property to multiply x-1 by 4.

$$y+2+4x-4=\left(x-1\right)\left(y+2\right)$$

Subtract 4 from 2 to get -2.

$$y-2+4x=\left(x-1\right)\left(y+2\right)$$

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

$$y-2+4x=xy+2x-y-2$$

Subtract xy from both sides.

$$y-2+4x-xy=2x-y-2$$

Add y to both sides.

$$y-2+4x-xy+y=2x-2$$

Combine y and y to get 2y.

$$2y-2+4x-xy=2x-2$$

Add 2 to both sides.

$$2y+4x-xy=2x-2+2$$

Add -2 and 2 to get 0.

$$2y+4x-xy=2x$$

Subtract 4x from both sides.

$$2y-xy=2x-4x$$

Combine 2x and -4x to get -2x.

$$2y-xy=-2x$$

Combine all terms containing y.

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

Divide both sides by -x+2.

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

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

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

Variable y cannot be equal to -2.

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