What is the answer to 1/x+1/x-4= 2/(x^2)-4x ?

The answer to 1/x+1/x-4= 2/(x^2)-4x is x=1,x= 1/(sqrt(2))i,x=-1/(sqrt(2))i

Solve for x: 1/x+1/x-4= 2/(x^2)-4x

The solution is x=1,x= 1/(sqrt(2))i,x=-1/(sqrt(2))i

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\frac{1}{x} + \frac{1}{x} - 4 = \frac{2}{x ^{2}} - 4 x

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

Solution steps

\frac{1}{x} + \frac{1}{x} - 4 = \frac{2}{x ^{2}} - 4 x

Multiply by LCM

2 x - 4 x^{2} = 2 - 4 x^{3}

Solve

2 x - 4 x^{2} = 2 - 4 x^{3} : x = 1, x = \frac{1}{2} i, x = - \frac{1}{2} i

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

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

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

\frac{x - 4}{x - 2} = \frac{- 3}{4}

\frac{( 1 ) x + 1}{x} = \frac{21}{20}

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

\frac{12}{30} = \frac{( 2 x )}{( 4 x + 10 )}

\frac{y ^{2}}{4 - 5 y + 16} = 0

What is the answer to 1/x+1/x-4= 2/(x^2)-4x ?
The answer to 1/x+1/x-4= 2/(x^2)-4x is x=1,x= 1/(sqrt(2))i,x=-1/(sqrt(2))i
Solve for x: 1/x+1/x-4= 2/(x^2)-4x
The solution is x=1,x= 1/(sqrt(2))i,x=-1/(sqrt(2))i