Solve x-9/x^2-9-1/2x+6=2/9-3x

$$\frac{ x-9 }{ { x }^{ 2 } -9 } - \frac{ 1 }{ 2x+6 } = \frac{ 2 }{ 9-3x }$$

Solve for x

$$x = \frac{33}{7} = 4\frac{5}{7} \approx 4.714285714$$

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 6\left(x-3\right)\left(x+3\right), the least common multiple of x^{2}-9,2x+6,9-3x.

$$6\left(x-9\right)-\left(3x-9\right)=\left(-6-2x\right)\times 2$$

Use the distributive property to multiply 6 by x-9.

$$6x-54-\left(3x-9\right)=\left(-6-2x\right)\times 2$$

To find the opposite of 3x-9, find the opposite of each term.

$$6x-54-3x+9=\left(-6-2x\right)\times 2$$

Combine 6x and -3x to get 3x.

$$3x-54+9=\left(-6-2x\right)\times 2$$

Add -54 and 9 to get -45.

$$3x-45=\left(-6-2x\right)\times 2$$

Use the distributive property to multiply -6-2x by 2.

$$3x-45=-12-4x$$

Add 4x to both sides.

$$3x-45+4x=-12$$

Combine 3x and 4x to get 7x.

$$7x-45=-12$$

Add 45 to both sides.

$$7x=-12+45$$

Add -12 and 45 to get 33.

$$7x=33$$

Divide both sides by 7.

$$x=\frac{33}{7}$$