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

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

Solve for x

$$x=\frac{2}{5}=0.4$$

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.

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

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

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

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

$$3x-6+x^{2}+2x=\left(x-2\right)\left(x+2\right)$$

Combine 3x and 2x to get 5x.

$$5x-6+x^{2}=\left(x-2\right)\left(x+2\right)$$

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.

$$5x-6+x^{2}=x^{2}-4$$

Subtract x^{2} from both sides.

$$5x-6+x^{2}-x^{2}=-4$$

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

$$5x-6=-4$$

Add 6 to both sides.

$$5x=-4+6$$

Add -4 and 6 to get 2.

$$5x=2$$

Divide both sides by 5.

$$x=\frac{2}{5}$$