Solve x/x-1-3/x=1

$$\frac{ x }{ x-1 } - \frac{ 3 }{ x } =1$$

Solve for x

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 0,1 since division by zero is not defined. Multiply both sides of the equation by x\left(x-1\right), the least common multiple of x-1,x.

$$xx-\left(x-1\right)\times 3=x\left(x-1\right)$$

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

$$x^{2}-\left(x-1\right)\times 3=x\left(x-1\right)$$

Use the distributive property to multiply x-1 by 3.

$$x^{2}-\left(3x-3\right)=x\left(x-1\right)$$

To find the opposite of 3x-3, find the opposite of each term.

$$x^{2}-3x+3=x\left(x-1\right)$$

Use the distributive property to multiply x by x-1.

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

Subtract x^{2} from both sides.

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

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

$$-3x+3=-x$$

Add x to both sides.

$$-3x+3+x=0$$

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

$$-2x+3=0$$

Subtract 3 from both sides. Anything subtracted from zero gives its negation.

$$-2x=-3$$

Divide both sides by -2.

$$x=\frac{-3}{-2}$$

Fraction \frac{-3}{-2} can be simplified to \frac{3}{2} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{3}{2}$$