Solve 2/x+9-3/x-9=2x/x^2-81

$$\frac { 2 } { x + 9 } - \frac { 3 } { x - 9 } = \frac { 2 x } { x ^ { 2 } - 81 }$$

Solve for x

$$x=-15$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -9,9 since division by zero is not defined. Multiply both sides of the equation by \left(x-9\right)\left(x+9\right), the least common multiple of x+9,x-9,x^{2}-81.

$$\left(x-9\right)\times 2-\left(x+9\right)\times 3=2x$$

Use the distributive property to multiply x-9 by 2.

$$2x-18-\left(x+9\right)\times 3=2x$$

Use the distributive property to multiply x+9 by 3.

$$2x-18-\left(3x+27\right)=2x$$

To find the opposite of 3x+27, find the opposite of each term.

$$2x-18-3x-27=2x$$

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

$$-x-18-27=2x$$

Subtract 27 from -18 to get -45.

$$-x-45=2x$$

Subtract 2x from both sides.

$$-x-45-2x=0$$

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

$$-3x-45=0$$

Add 45 to both sides. Anything plus zero gives itself.

$$-3x=45$$

Divide both sides by -3.

$$x=\frac{45}{-3}$$

Divide 45 by -3 to get -15.

$$x=-15$$