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

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

Solve for y (complex solution)

$$y=1-x^{2}$$

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

Steps for Solving Linear Equation

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

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

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

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

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

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

To find the opposite of xy+y, find the opposite of each term.

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

Combine xy and -xy to get 0.

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

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

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

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

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

Use the distributive property to multiply 2x-2 by x+1 and combine like terms.

$$-2y=2x^{2}-2$$

Divide both sides by -2.

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

Dividing by -2 undoes the multiplication by -2.

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

Divide 2x^{2}-2 by -2.

$$y=1-x^{2}$$

Solve for y

$$y=1-x^{2}$$

$$|x|\neq 1$$

Steps for Solving Linear Equation

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

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

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

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

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

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

To find the opposite of xy+y, find the opposite of each term.

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

Combine xy and -xy to get 0.

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

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

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

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

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

Use the distributive property to multiply 2x-2 by x+1 and combine like terms.

$$-2y=2x^{2}-2$$

Divide both sides by -2.

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

Dividing by -2 undoes the multiplication by -2.

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

Divide 2x^{2}-2 by -2.

$$y=1-x^{2}$$

Solve for x (complex solution)

$$x=-\sqrt{1-y}$$

$$x=\sqrt{1-y}\text{, }y\neq 0$$

Solve for x

$$x=\sqrt{1-y}$$

$$x=-\sqrt{1-y}\text{, }y\neq 0\text{ and }y\leq 1$$