Solve Phi2/x+1-2x/1-x^2=1/x-1

$$\Phi \frac { 2 } { x + 1 } - \frac { 2 x } { 1 - x ^ { 2 } } = \frac { 1 } { x - 1 }$$

Solve for x (complex solution)

$$x\in \mathrm{C}\setminus 1,-1$$

$$\Phi =-\frac{1}{2}$$

Steps for Solving Linear Equation

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

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

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

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

Use the distributive property to multiply \Phi x-\Phi by 2.

$$2\Phi x-2\Phi +2x=x+1$$

Subtract x from both sides.

$$2\Phi x-2\Phi +2x-x=1$$

Combine 2x and -x to get x.

$$2\Phi x-2\Phi +x=1$$

Add 2\Phi to both sides.

$$2\Phi x+x=1+2\Phi$$

Combine all terms containing x.

$$\left(2\Phi +1\right)x=1+2\Phi$$

The equation is in standard form.

$$\left(2\Phi +1\right)x=2\Phi +1$$

Divide both sides by 1+2\Phi .

$$\frac{\left(2\Phi +1\right)x}{2\Phi +1}=\frac{2\Phi +1}{2\Phi +1}$$

Dividing by 1+2\Phi undoes the multiplication by 1+2\Phi .

$$x=\frac{2\Phi +1}{2\Phi +1}$$

Divide 1+2\Phi by 1+2\Phi .

$$x=1$$

Variable x cannot be equal to 1.

$$x\in \emptyset$$

Solve for Φ (complex solution)

$$\Phi =-\frac{1}{2}$$

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

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+1,1-x^{2},x-1.

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

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

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

Use the distributive property to multiply \Phi x-\Phi by 2.

$$2\Phi x-2\Phi +2x=x+1$$

Subtract 2x from both sides.

$$2\Phi x-2\Phi =x+1-2x$$

Combine x and -2x to get -x.

$$2\Phi x-2\Phi =-x+1$$

Combine all terms containing \Phi .

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

The equation is in standard form.

$$\left(2x-2\right)\Phi =1-x$$

Divide both sides by 2x-2.

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

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

$$\Phi =\frac{1-x}{2x-2}$$

Divide -x+1 by 2x-2.

$$\Phi =-\frac{1}{2}$$

Solve for x

$$x\in \mathrm{R}\setminus 1,-1$$

$$\Phi =-\frac{1}{2}$$

Steps for Solving Linear Equation

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

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

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

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

Use the distributive property to multiply \Phi x-\Phi by 2.

$$2\Phi x-2\Phi +2x=x+1$$

Subtract x from both sides.

$$2\Phi x-2\Phi +2x-x=1$$

Combine 2x and -x to get x.

$$2\Phi x-2\Phi +x=1$$

Add 2\Phi to both sides.

$$2\Phi x+x=1+2\Phi$$

Combine all terms containing x.

$$\left(2\Phi +1\right)x=1+2\Phi$$

The equation is in standard form.

$$\left(2\Phi +1\right)x=2\Phi +1$$

Divide both sides by 1+2\Phi .

$$\frac{\left(2\Phi +1\right)x}{2\Phi +1}=\frac{2\Phi +1}{2\Phi +1}$$

Dividing by 1+2\Phi undoes the multiplication by 1+2\Phi .

$$x=\frac{2\Phi +1}{2\Phi +1}$$

Divide 1+2\Phi by 1+2\Phi .

$$x=1$$

Variable x cannot be equal to 1.

$$x\in \emptyset$$

Solve for Φ

$$\Phi =-\frac{1}{2}$$

$$|x|\neq 1$$

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+1,1-x^{2},x-1.

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

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

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

Use the distributive property to multiply \Phi x-\Phi by 2.

$$2\Phi x-2\Phi +2x=x+1$$

Subtract 2x from both sides.

$$2\Phi x-2\Phi =x+1-2x$$

Combine x and -2x to get -x.

$$2\Phi x-2\Phi =-x+1$$

Combine all terms containing \Phi .

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

The equation is in standard form.

$$\left(2x-2\right)\Phi =1-x$$

Divide both sides by 2x-2.

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

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

$$\Phi =\frac{1-x}{2x-2}$$

Divide -x+1 by 2x-2.

$$\Phi =-\frac{1}{2}$$