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

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

Solve for x

$$x=\frac{2}{7}\approx 0.285714286$$

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.

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

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

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

Use the distributive property to multiply 2x-4 by x.

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

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

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

To find the opposite of 3x+6, find the opposite of each term.

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

Combine -4x and -3x to get -7x.

$$2x^{2}-7x-6=2\left(x-2\right)\left(x+2\right)$$

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

$$2x^{2}-7x-6=\left(2x-4\right)\left(x+2\right)$$

Use the distributive property to multiply 2x-4 by x+2 and combine like terms.

$$2x^{2}-7x-6=2x^{2}-8$$

Subtract 2x^{2} from both sides.

$$2x^{2}-7x-6-2x^{2}=-8$$

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

$$-7x-6=-8$$

Add 6 to both sides.

$$-7x=-8+6$$

Add -8 and 6 to get -2.

$$-7x=-2$$

Divide both sides by -7.

$$x=\frac{-2}{-7}$$

Fraction \frac{-2}{-7} can be simplified to \frac{2}{7} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{2}{7}$$