Solve 3/x-1=2-x/x-x^2-1/2x

$$\frac { 3 } { x - 1 } = \frac { 2 - x } { x - x ^ { 2 } } - \frac { 1 } { 2 x }$$

Solve for x

$$x=-\frac{3}{5}=-0.6$$

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 2x\left(x-1\right), the least common multiple of x-1,x-x^{2},2x.

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

Multiply 2 and 3 to get 6.

$$6x=-2\left(2-x\right)-\left(x-1\right)$$

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

$$6x=-4+2x-\left(x-1\right)$$

To find the opposite of x-1, find the opposite of each term.

$$6x=-4+2x-x+1$$

Combine 2x and -x to get x.

$$6x=-4+x+1$$

Add -4 and 1 to get -3.

$$6x=-3+x$$

Subtract x from both sides.

$$6x-x=-3$$

Combine 6x and -x to get 5x.

$$5x=-3$$

Divide both sides by 5.

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

Fraction \frac{-3}{5} can be rewritten as -\frac{3}{5} by extracting the negative sign.

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