Solve 3/x-3=-4/x+3+11/(x-3)(x+3)

$$\frac { 3 } { x - 3 } = \frac { - 4 } { x + 3 } + \frac { 11 } { ( x - 3 ) ( x + 3 ) }$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -3,3 since division by zero is not defined. Multiply both sides of the equation by \left(x-3\right)\left(x+3\right), the least common multiple of x-3,x+3,\left(x-3\right)\left(x+3\right).

$$\left(x+3\right)\times 3=\left(x-3\right)\left(-4\right)+11$$

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

$$3x+9=\left(x-3\right)\left(-4\right)+11$$

Use the distributive property to multiply x-3 by -4.

$$3x+9=-4x+12+11$$

Add 12 and 11 to get 23.

$$3x+9=-4x+23$$

Add 4x to both sides.

$$3x+9+4x=23$$

Combine 3x and 4x to get 7x.

$$7x+9=23$$

Subtract 9 from both sides.

$$7x=23-9$$

Subtract 9 from 23 to get 14.

$$7x=14$$

Divide both sides by 7.

$$x=\frac{14}{7}$$

Divide 14 by 7 to get 2.

$$x=2$$