Solve 6/x^2-100=2/x+10-4/x-10

$$\frac { 6 } { x ^ { 2 } - 100 } = \frac { 2 } { x + 10 } - \frac { 4 } { x - 10 }$$

Solve for x

$$x=-33$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -10,10 since division by zero is not defined. Multiply both sides of the equation by \left(x-10\right)\left(x+10\right), the least common multiple of x^{2}-100,x+10,x-10.

$$6=\left(x-10\right)\times 2-\left(x+10\right)\times 4$$

Use the distributive property to multiply x-10 by 2.

$$6=2x-20-\left(x+10\right)\times 4$$

Use the distributive property to multiply x+10 by 4.

$$6=2x-20-\left(4x+40\right)$$

To find the opposite of 4x+40, find the opposite of each term.

$$6=2x-20-4x-40$$

Combine 2x and -4x to get -2x.

$$6=-2x-20-40$$

Subtract 40 from -20 to get -60.

$$6=-2x-60$$

Swap sides so that all variable terms are on the left hand side.

$$-2x-60=6$$

Add 60 to both sides.

$$-2x=6+60$$

Add 6 and 60 to get 66.

$$-2x=66$$

Divide both sides by -2.

$$x=\frac{66}{-2}$$

Divide 66 by -2 to get -33.

$$x=-33$$