Solve x-2/x-5=x/x-1

$$\frac{ x-2 }{ x-5 } = \frac{ x }{ x-1 }$$

Solve for x

$$x=-1$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 1,5 since division by zero is not defined. Multiply both sides of the equation by \left(x-5\right)\left(x-1\right), the least common multiple of x-5,x-1.

$$\left(x-1\right)\left(x-2\right)=\left(x-5\right)x$$

Use the distributive property to multiply x-1 by x-2 and combine like terms.

$$x^{2}-3x+2=\left(x-5\right)x$$

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

$$x^{2}-3x+2=x^{2}-5x$$

Subtract x^{2} from both sides.

$$x^{2}-3x+2-x^{2}=-5x$$

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

$$-3x+2=-5x$$

Add 5x to both sides.

$$-3x+2+5x=0$$

Combine -3x and 5x to get 2x.

$$2x+2=0$$

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

$$2x=-2$$

Divide both sides by 2.

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

Divide -2 by 2 to get -1.

$$x=-1$$