Solve 1/w^2-4-4/w-2=1/w+2

$$\frac { 1 } { w ^ { 2 } - 4 } - \frac { 4 } { w - 2 } = \frac { 1 } { w + 2 }$$

Solve for w

$$w=-1$$

Steps for Solving Linear Equation

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

$$1-\left(w+2\right)\times 4=w-2$$

Use the distributive property to multiply w+2 by 4.

$$1-\left(4w+8\right)=w-2$$

To find the opposite of 4w+8, find the opposite of each term.

$$1-4w-8=w-2$$

Subtract 8 from 1 to get -7.

$$-7-4w=w-2$$

Subtract w from both sides.

$$-7-4w-w=-2$$

Combine -4w and -w to get -5w.

$$-7-5w=-2$$

Add 7 to both sides.

$$-5w=-2+7$$

Add -2 and 7 to get 5.

$$-5w=5$$

Divide both sides by -5.

$$w=\frac{5}{-5}$$

Divide 5 by -5 to get -1.

$$w=-1$$