Solve x-4/x+4+x+5/x-5=2xleft(x+5right)/x^2-x-20

$$\frac{ x-4 }{ x+4 } + \frac{ x+5 }{ x-5 } = \frac{ 2x \left( x+5 \right) }{ { x }^{ 2 } -x-20 }$$

Solve for x

$$x=4$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -4,5 since division by zero is not defined. Multiply both sides of the equation by \left(x-5\right)\left(x+4\right), the least common multiple of x+4,x-5,x^{2}-x-20.

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

Use the distributive property to multiply x-5 by x-4 and combine like terms.

$$x^{2}-9x+20+\left(x+4\right)\left(x+5\right)=2x\left(x+5\right)$$

Use the distributive property to multiply x+4 by x+5 and combine like terms.

$$x^{2}-9x+20+x^{2}+9x+20=2x\left(x+5\right)$$

Combine x^{2} and x^{2} to get 2x^{2}.

$$2x^{2}-9x+20+9x+20=2x\left(x+5\right)$$

Combine -9x and 9x to get 0.

$$2x^{2}+20+20=2x\left(x+5\right)$$

Add 20 and 20 to get 40.

$$2x^{2}+40=2x\left(x+5\right)$$

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

$$2x^{2}+40=2x^{2}+10x$$

Subtract 2x^{2} from both sides.

$$2x^{2}+40-2x^{2}=10x$$

Combine 2x^{2} and -2x^{2} to get 0.

$$40=10x$$

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

$$10x=40$$

Divide both sides by 10.

$$x=\frac{40}{10}$$

Divide 40 by 10 to get 4.

$$x=4$$