Solve x+p/2+p=x-p/2-p

$$\frac { x + p } { 2 + p } = \frac { x - p } { 2 - p }$$

Solve for p (complex solution)

$$\left\{\begin{matrix}\\p=0\text{, }&\text{unconditionally}\\p\in \mathrm{C}\setminus -2,2\text{, }&x=2\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$\left(p-2\right)\left(x+p\right)=-\left(2+p\right)\left(x-p\right)$$

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

$$px+p^{2}-2x-2p=-\left(2+p\right)\left(x-p\right)$$

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

$$px+p^{2}-2x-2p=\left(-2-p\right)\left(x-p\right)$$

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

$$px+p^{2}-2x-2p=-2x+2p-px+p^{2}$$

Subtract 2p from both sides.

$$px+p^{2}-2x-2p-2p=-2x-px+p^{2}$$

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

$$px+p^{2}-2x-4p=-2x-px+p^{2}$$

Add px to both sides.

$$px+p^{2}-2x-4p+px=-2x+p^{2}$$

Combine px and px to get 2px.

$$2px+p^{2}-2x-4p=-2x+p^{2}$$

Subtract p^{2} from both sides.

$$2px+p^{2}-2x-4p-p^{2}=-2x$$

Combine p^{2} and -p^{2} to get 0.

$$2px-2x-4p=-2x$$

Add 2x to both sides.

$$2px-4p=-2x+2x$$

Combine -2x and 2x to get 0.

$$2px-4p=0$$

Combine all terms containing p.

$$\left(2x-4\right)p=0$$

Divide 0 by 2x-4.

$$p=0$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=2\text{, }&p\neq -2\text{ and }p\neq 2\\x\in \mathrm{C}\text{, }&p=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(p-2\right)\left(p+2\right), the least common multiple of 2+p,2-p.

$$\left(p-2\right)\left(x+p\right)=-\left(2+p\right)\left(x-p\right)$$

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

$$px+p^{2}-2x-2p=-\left(2+p\right)\left(x-p\right)$$

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

$$px+p^{2}-2x-2p=\left(-2-p\right)\left(x-p\right)$$

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

$$px+p^{2}-2x-2p=-2x+2p-px+p^{2}$$

Add 2x to both sides.

$$px+p^{2}-2x-2p+2x=2p-px+p^{2}$$

Combine -2x and 2x to get 0.

$$px+p^{2}-2p=2p-px+p^{2}$$

Add px to both sides.

$$px+p^{2}-2p+px=2p+p^{2}$$

Combine px and px to get 2px.

$$2px+p^{2}-2p=2p+p^{2}$$

Subtract p^{2} from both sides.

$$2px-2p=2p+p^{2}-p^{2}$$

Combine p^{2} and -p^{2} to get 0.

$$2px-2p=2p$$

Add 2p to both sides.

$$2px=2p+2p$$

Combine 2p and 2p to get 4p.

$$2px=4p$$

Divide both sides by 2p.

$$\frac{2px}{2p}=\frac{4p}{2p}$$

Dividing by 2p undoes the multiplication by 2p.

$$x=\frac{4p}{2p}$$

Divide 4p by 2p.

$$x=2$$

Solve for p

$$\left\{\begin{matrix}\\p=0\text{, }&\text{unconditionally}\\p\in \mathrm{R}\setminus -2,2\text{, }&x=2\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$\left(p-2\right)\left(x+p\right)=-\left(2+p\right)\left(x-p\right)$$

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

$$px+p^{2}-2x-2p=-\left(2+p\right)\left(x-p\right)$$

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

$$px+p^{2}-2x-2p=\left(-2-p\right)\left(x-p\right)$$

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

$$px+p^{2}-2x-2p=-2x+2p-px+p^{2}$$

Subtract 2p from both sides.

$$px+p^{2}-2x-2p-2p=-2x-px+p^{2}$$

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

$$px+p^{2}-2x-4p=-2x-px+p^{2}$$

Add px to both sides.

$$px+p^{2}-2x-4p+px=-2x+p^{2}$$

Combine px and px to get 2px.

$$2px+p^{2}-2x-4p=-2x+p^{2}$$

Subtract p^{2} from both sides.

$$2px+p^{2}-2x-4p-p^{2}=-2x$$

Combine p^{2} and -p^{2} to get 0.

$$2px-2x-4p=-2x$$

Add 2x to both sides.

$$2px-4p=-2x+2x$$

Combine -2x and 2x to get 0.

$$2px-4p=0$$

Combine all terms containing p.

$$\left(2x-4\right)p=0$$

Divide 0 by 2x-4.

$$p=0$$

Solve for x

$$\left\{\begin{matrix}x=2\text{, }&|p|\neq 2\\x\in \mathrm{R}\text{, }&p=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(p-2\right)\left(p+2\right), the least common multiple of 2+p,2-p.

$$\left(p-2\right)\left(x+p\right)=-\left(2+p\right)\left(x-p\right)$$

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

$$px+p^{2}-2x-2p=-\left(2+p\right)\left(x-p\right)$$

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

$$px+p^{2}-2x-2p=\left(-2-p\right)\left(x-p\right)$$

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

$$px+p^{2}-2x-2p=-2x+2p-px+p^{2}$$

Add 2x to both sides.

$$px+p^{2}-2x-2p+2x=2p-px+p^{2}$$

Combine -2x and 2x to get 0.

$$px+p^{2}-2p=2p-px+p^{2}$$

Add px to both sides.

$$px+p^{2}-2p+px=2p+p^{2}$$

Combine px and px to get 2px.

$$2px+p^{2}-2p=2p+p^{2}$$

Subtract p^{2} from both sides.

$$2px-2p=2p+p^{2}-p^{2}$$

Combine p^{2} and -p^{2} to get 0.

$$2px-2p=2p$$

Add 2p to both sides.

$$2px=2p+2p$$

Combine 2p and 2p to get 4p.

$$2px=4p$$

Divide both sides by 2p.

$$\frac{2px}{2p}=\frac{4p}{2p}$$

Dividing by 2p undoes the multiplication by 2p.

$$x=\frac{4p}{2p}$$

Divide 4p by 2p.

$$x=2$$