Solve 3+x=1+4/2-x

$$3+x=1+ \frac{ 4 }{ 2-x }$$

Solve for x

$$x=0$$

Steps by Finding Square Root

Variable x cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by -x+2.

$$\left(-x+2\right)\times 3+\left(-x+2\right)x=-x+2+4$$

Use the distributive property to multiply -x+2 by 3.

$$-3x+6+\left(-x+2\right)x=-x+2+4$$

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

$$-3x+6-x^{2}+2x=-x+2+4$$

Combine -3x and 2x to get -x.

$$-x+6-x^{2}=-x+2+4$$

Add 2 and 4 to get 6.

$$-x+6-x^{2}=-x+6$$

Add x to both sides.

$$-x+6-x^{2}+x=6$$

Combine -x and x to get 0.

$$6-x^{2}=6$$

Subtract 6 from both sides.

$$-x^{2}=6-6$$

Subtract 6 from 6 to get 0.

$$-x^{2}=0$$

Divide both sides by -1. Zero divided by any non-zero number gives zero.

$$x^{2}=0$$

Take the square root of both sides of the equation.

$$x=0 x=0$$

The equation is now solved. Solutions are the same.

$$x=0$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by -x+2.

$$\left(-x+2\right)\times 3+\left(-x+2\right)x=-x+2+4$$

Use the distributive property to multiply -x+2 by 3.

$$-3x+6+\left(-x+2\right)x=-x+2+4$$

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

$$-3x+6-x^{2}+2x=-x+2+4$$

Combine -3x and 2x to get -x.

$$-x+6-x^{2}=-x+2+4$$

Add 2 and 4 to get 6.

$$-x+6-x^{2}=-x+6$$

Add x to both sides.

$$-x+6-x^{2}+x=6$$

Combine -x and x to get 0.

$$6-x^{2}=6$$

Subtract 6 from both sides.

$$6-x^{2}-6=0$$

Subtract 6 from 6 to get 0.

$$-x^{2}=0$$

Divide both sides by -1. Zero divided by any non-zero number gives zero.

$$x^{2}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}}}{2}$$

Take the square root of 0^{2}.

$$x=\frac{0±0}{2}$$

Divide 0 by 2.

$$x=0$$