Solve 5x+1/x-1=3(2x-1)/2(x-1)

$$\frac { 5 x + 1 } { x - 1 } = \frac { 3 ( 2 x - 1 ) } { 2 ( x - 1 ) }$$

Solve for x

$$x = -\frac{5}{4} = -1\frac{1}{4} = -1.25$$

Steps for Solving Linear Equation

Variable x cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by 2\left(x-1\right), the least common multiple of x-1,2\left(x-1\right).

$$2\left(5x+1\right)=3\left(2x-1\right)$$

Use the distributive property to multiply 2 by 5x+1.

$$10x+2=3\left(2x-1\right)$$

Use the distributive property to multiply 3 by 2x-1.

$$10x+2=6x-3$$

Subtract 6x from both sides.

$$10x+2-6x=-3$$

Combine 10x and -6x to get 4x.

$$4x+2=-3$$

Subtract 2 from both sides.

$$4x=-3-2$$

Subtract 2 from -3 to get -5.

$$4x=-5$$

Divide both sides by 4.

$$x=\frac{-5}{4}$$

Fraction \frac{-5}{4} can be rewritten as -\frac{5}{4} by extracting the negative sign.

$$x=-\frac{5}{4}$$