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

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

Solve for x

$$x = -\frac{6}{5} = -1\frac{1}{5} = -1.2$$

Steps for Solving Linear Equation

Variable x 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(x-2\right)\left(x+2\right), the least common multiple of x-2,x+2.

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

Multiply x+2 and x+2 to get \left(x+2\right)^{2}.

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

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+2\right)^{2}.

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

Combine 4x and x to get 5x.

$$x^{2}+5x+4-2=\left(x-2\right)\left(x+2\right)$$

Subtract 2 from 4 to get 2.

$$x^{2}+5x+2=\left(x-2\right)\left(x+2\right)$$

Consider \left(x-2\right)\left(x+2\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.

$$x^{2}+5x+2=x^{2}-4$$

Subtract x^{2} from both sides.

$$x^{2}+5x+2-x^{2}=-4$$

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

$$5x+2=-4$$

Subtract 2 from both sides.

$$5x=-4-2$$

Subtract 2 from -4 to get -6.

$$5x=-6$$

Divide both sides by 5.

$$x=\frac{-6}{5}$$

Fraction \frac{-6}{5} can be rewritten as -\frac{6}{5} by extracting the negative sign.

$$x=-\frac{6}{5}$$