Solve 5x/x^2-4-4/x+2=3/x-2

$$\frac { 5 x } { x ^ { 2 } - 4 } - \frac { 4 } { x + 2 } = \frac { 3 } { x - 2 }$$

Solve for x

$$x=1$$

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}-4,x+2,x-2.

$$5x-\left(x-2\right)\times 4=\left(x+2\right)\times 3$$

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

$$5x-\left(4x-8\right)=\left(x+2\right)\times 3$$

To find the opposite of 4x-8, find the opposite of each term.

$$5x-4x+8=\left(x+2\right)\times 3$$

Combine 5x and -4x to get x.

$$x+8=\left(x+2\right)\times 3$$

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

$$x+8=3x+6$$

Subtract 3x from both sides.

$$x+8-3x=6$$

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

$$-2x+8=6$$

Subtract 8 from both sides.

$$-2x=6-8$$

Subtract 8 from 6 to get -2.

$$-2x=-2$$

Divide both sides by -2.

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

Divide -2 by -2 to get 1.

$$x=1$$