Solve 3/x-2=-4/x+6+38/(x-2)(x+6)

$$\frac { 3 } { x - 2 } = \frac { - 4 } { x + 6 } + \frac { 38 } { ( x - 2 ) ( x + 6 ) }$$

Solve for x

$$x=4$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -6,2 since division by zero is not defined. Multiply both sides of the equation by \left(x-2\right)\left(x+6\right), the least common multiple of x-2,x+6,\left(x-2\right)\left(x+6\right).

$$\left(x+6\right)\times 3=\left(x-2\right)\left(-4\right)+38$$

Use the distributive property to multiply x+6 by 3.

$$3x+18=\left(x-2\right)\left(-4\right)+38$$

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

$$3x+18=-4x+8+38$$

Add 8 and 38 to get 46.

$$3x+18=-4x+46$$

Add 4x to both sides.

$$3x+18+4x=46$$

Combine 3x and 4x to get 7x.

$$7x+18=46$$

Subtract 18 from both sides.

$$7x=46-18$$

Subtract 18 from 46 to get 28.

$$7x=28$$

Divide both sides by 7.

$$x=\frac{28}{7}$$

Divide 28 by 7 to get 4.

$$x=4$$