Solve 2/x-5-4/x+5=6/x^2-25

$$\frac { 2 } { x - 5 } - \frac { 4 } { x + 5 } = \frac { 6 } { x ^ { 2 } - 25 }$$

Solve for x

$$x=12$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -5,5 since division by zero is not defined. Multiply both sides of the equation by \left(x-5\right)\left(x+5\right), the least common multiple of x-5,x+5,x^{2}-25.

$$\left(x+5\right)\times 2-\left(x-5\right)\times 4=6$$

Use the distributive property to multiply x+5 by 2.

$$2x+10-\left(x-5\right)\times 4=6$$

Use the distributive property to multiply x-5 by 4.

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

To find the opposite of 4x-20, find the opposite of each term.

$$2x+10-4x+20=6$$

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

$$-2x+10+20=6$$

Add 10 and 20 to get 30.

$$-2x+30=6$$

Subtract 30 from both sides.

$$-2x=6-30$$

Subtract 30 from 6 to get -24.

$$-2x=-24$$

Divide both sides by -2.

$$x=\frac{-24}{-2}$$

Divide -24 by -2 to get 12.

$$x=12$$