Solve 3/x-1=5/x

$$\frac{ 3 }{ x-1 } = \frac{ 5 }{ x }$$

Solve for x

$$x = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

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.

$$x\times 3=\left(x-1\right)\times 5$$

Use the distributive property to multiply x-1 by 5.

$$x\times 3=5x-5$$

Subtract 5x from both sides.

$$x\times 3-5x=-5$$

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

$$-2x=-5$$

Divide both sides by -2.

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

Fraction \frac{-5}{-2} can be simplified to \frac{5}{2} by removing the negative sign from both the numerator and the denominator.

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