Solve 4/x-4=-6/x+2+14/(x-4)(x+2)

$$\frac { 4 } { x - 4 } = \frac { - 6 } { x + 2 } + \frac { 14 } { ( x - 4 ) ( x + 2 ) }$$

Solve for x

$$x=3$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -2,4 since division by zero is not defined. Multiply both sides of the equation by \left(x-4\right)\left(x+2\right), the least common multiple of x-4,x+2,\left(x-4\right)\left(x+2\right).

$$\left(x+2\right)\times 4=\left(x-4\right)\left(-6\right)+14$$

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

$$4x+8=\left(x-4\right)\left(-6\right)+14$$

Use the distributive property to multiply x-4 by -6.

$$4x+8=-6x+24+14$$

Add 24 and 14 to get 38.

$$4x+8=-6x+38$$

Add 6x to both sides.

$$4x+8+6x=38$$

Combine 4x and 6x to get 10x.

$$10x+8=38$$

Subtract 8 from both sides.

$$10x=38-8$$

Subtract 8 from 38 to get 30.

$$10x=30$$

Divide both sides by 10.

$$x=\frac{30}{10}$$

Divide 30 by 10 to get 3.

$$x=3$$