Solve 1/3x+6-4/x^2-4=7/x-2

$$\frac { 1 } { 3 x + 6 } - \frac { 4 } { x ^ { 2 } - 4 } = \frac { 7 } { x - 2 }$$

Solve for x

$$x = -\frac{14}{5} = -2\frac{4}{5} = -2.8$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -2,2 since division by zero is not defined. Multiply both sides of the equation by 3\left(x-2\right)\left(x+2\right), the least common multiple of 3x+6,x^{2}-4,x-2.

$$x-2-3\times 4=\left(3x+6\right)\times 7$$

Multiply -3 and 4 to get -12.

$$x-2-12=\left(3x+6\right)\times 7$$

Subtract 12 from -2 to get -14.

$$x-14=\left(3x+6\right)\times 7$$

Use the distributive property to multiply 3x+6 by 7.

$$x-14=21x+42$$

Subtract 21x from both sides.

$$x-14-21x=42$$

Combine x and -21x to get -20x.

$$-20x-14=42$$

Add 14 to both sides.

$$-20x=42+14$$

Add 42 and 14 to get 56.

$$-20x=56$$

Divide both sides by -20.

$$x=\frac{56}{-20}$$

Reduce the fraction \frac{56}{-20} to lowest terms by extracting and canceling out 4.

$$x=-\frac{14}{5}$$