Solve x+10/x=x-5/x+10

$$\frac { x + 10 } { x } = \frac { x - 5 } { x + 10 }$$

Solve for x

$$x=-4$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -10,0 since division by zero is not defined. Multiply both sides of the equation by x\left(x+10\right), the least common multiple of x,x+10.

$$\left(x+10\right)\left(x+10\right)=x\left(x-5\right)$$

Multiply x+10 and x+10 to get \left(x+10\right)^{2}.

$$\left(x+10\right)^{2}=x\left(x-5\right)$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+10\right)^{2}.

$$x^{2}+20x+100=x\left(x-5\right)$$

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

$$x^{2}+20x+100=x^{2}-5x$$

Subtract x^{2} from both sides.

$$x^{2}+20x+100-x^{2}=-5x$$

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

$$20x+100=-5x$$

Add 5x to both sides.

$$20x+100+5x=0$$

Combine 20x and 5x to get 25x.

$$25x+100=0$$

Subtract 100 from both sides. Anything subtracted from zero gives its negation.

$$25x=-100$$

Divide both sides by 25.

$$x=\frac{-100}{25}$$

Divide -100 by 25 to get -4.

$$x=-4$$