Solve x/x-10+x/x^2-100=x+11/x+10

$$\frac { x } { x - 10 } + \frac { x } { x ^ { 2 } - 100 } = \frac { x + 11 } { x + 10 }$$

Solve for x

$$x=-11$$

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-10,x^{2}-100,x+10.

$$\left(x+10\right)x+x=\left(x-10\right)\left(x+11\right)$$

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

$$x^{2}+10x+x=\left(x-10\right)\left(x+11\right)$$

Combine 10x and x to get 11x.

$$x^{2}+11x=\left(x-10\right)\left(x+11\right)$$

Use the distributive property to multiply x-10 by x+11 and combine like terms.

$$x^{2}+11x=x^{2}+x-110$$

Subtract x^{2} from both sides.

$$x^{2}+11x-x^{2}=x-110$$

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

$$11x=x-110$$

Subtract x from both sides.

$$11x-x=-110$$

Combine 11x and -x to get 10x.

$$10x=-110$$

Divide both sides by 10.

$$x=\frac{-110}{10}$$

Divide -110 by 10 to get -11.

$$x=-11$$