Solve (2+x)(2-x)/3-x=1+x

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

Solve for x

$$x=\frac{1}{2}=0.5$$

Steps for Solving Linear Equation

Variable x cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by -x+3.

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

Consider \left(2+x\right)\left(2-x\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 2.

$$4-x^{2}=-x+3+\left(-x+3\right)x$$

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

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

Combine -x and 3x to get 2x.

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

Subtract 2x from both sides.

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

Add x^{2} to both sides.

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

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

$$4-2x=3$$

Subtract 4 from both sides.

$$-2x=3-4$$

Subtract 4 from 3 to get -1.

$$-2x=-1$$

Divide both sides by -2.

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

Fraction \frac{-1}{-2} can be simplified to \frac{1}{2} by removing the negative sign from both the numerator and the denominator.

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