Solve 4/x+5-8/x-5=4/x^2-25

$$\frac { 4 } { x + 5 } - \frac { 8 } { x - 5 } = \frac { 4 } { x ^ { 2 } - 25 }$$

Solve for x

$$x=-16$$

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.

$$\left(x-5\right)\times 4-\left(x+5\right)\times 8=4$$

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

$$4x-20-\left(x+5\right)\times 8=4$$

Use the distributive property to multiply x+5 by 8.

$$4x-20-\left(8x+40\right)=4$$

To find the opposite of 8x+40, find the opposite of each term.

$$4x-20-8x-40=4$$

Combine 4x and -8x to get -4x.

$$-4x-20-40=4$$

Subtract 40 from -20 to get -60.

$$-4x-60=4$$

Add 60 to both sides.

$$-4x=4+60$$

Add 4 and 60 to get 64.

$$-4x=64$$

Divide both sides by -4.

$$x=\frac{64}{-4}$$

Divide 64 by -4 to get -16.

$$x=-16$$