Solve 75/x-2-12x+6/x^2-4=18/x+2

$$\frac { 75 } { x - 2 } - \frac { 12 x + 6 } { x ^ { 2 } - 4 } = \frac { 18 } { x + 2 }$$

Solve for x

$$x=-4$$

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}-4,x+2.

$$\left(x+2\right)\times 75-\left(12x+6\right)=\left(x-2\right)\times 18$$

Use the distributive property to multiply x+2 by 75.

$$75x+150-\left(12x+6\right)=\left(x-2\right)\times 18$$

To find the opposite of 12x+6, find the opposite of each term.

$$75x+150-12x-6=\left(x-2\right)\times 18$$

Combine 75x and -12x to get 63x.

$$63x+150-6=\left(x-2\right)\times 18$$

Subtract 6 from 150 to get 144.

$$63x+144=\left(x-2\right)\times 18$$

Use the distributive property to multiply x-2 by 18.

$$63x+144=18x-36$$

Subtract 18x from both sides.

$$63x+144-18x=-36$$

Combine 63x and -18x to get 45x.

$$45x+144=-36$$

Subtract 144 from both sides.

$$45x=-36-144$$

Subtract 144 from -36 to get -180.

$$45x=-180$$

Divide both sides by 45.

$$x=\frac{-180}{45}$$

Divide -180 by 45 to get -4.

$$x=-4$$