What is the answer to (x^2-x)/(3x+1)=(-x)/(2x-1) ?

The answer to (x^2-x)/(3x+1)=(-x)/(2x-1) is x=0,x=i,x=-i

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(x^2-x)/(3x+1)=(-x)/(2x-1)

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

x = 0, x = i, x = - i

Solution steps

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

Cross multiply

(x^{2} - x) (2 x - 1) = - (3 x + 1) x

Solve

(x^{2} - x) (2 x - 1) = - (3 x + 1) x : x = 0, x = i, x = - i

x = 0, x = i, x = - i

Verify Solutions

Find undefined (singularity) points:

x = - \frac{1}{3}, x = \frac{1}{2}

Combine undefined points with solutions:

x = 0, x = i, x = - i

6 - \frac{4}{x ^{2}} = 0

x, y = \frac{x - t}{x + t}

\frac{x - 119}{x + 7} = - 5

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

\frac{4 x}{x ^{2} - 25} = \frac{1}{5 - x}

What is the answer to (x^2-x)/(3x+1)=(-x)/(2x-1) ?
The answer to (x^2-x)/(3x+1)=(-x)/(2x-1) is x=0,x=i,x=-i
Solve for x: (x^2-x)/(3x+1)=(-x)/(2x-1)
The solution is x=0,x=i,x=-i