What is the answer to x^{-2}+x^{-1}-12=0 ?

The answer to x^{-2}+x^{-1}-12=0 is x=-1/4 ,x= 1/3

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x^{-2}+x^{-1}-12=0

x^{- 2} + x^{- 1} - 12 = 0

x = - \frac{1}{4}, x = \frac{1}{3}

Solution steps

x^{- 2} + x^{- 1} - 12 = 0

Refine

\frac{1}{x ^{2}} + \frac{1}{x} - 12 = 0

Multiply by LCM

1 + x - 12 x^{2} = 0

Solve

1 + x - 12 x^{2} = 0 : x = - \frac{1}{4}, x = \frac{1}{3}

x = - \frac{1}{4}, x = \frac{1}{3}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = - \frac{1}{4}, x = \frac{1}{3}

\frac{c ^{2} + c}{c - 1} = 6

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

x, y = \frac{x - 3}{x + 4}

\frac{y}{2} - \frac{4}{y} = 1

x, z = \frac{y}{x}

What is the answer to x^{-2}+x^{-1}-12=0 ?
The answer to x^{-2}+x^{-1}-12=0 is x=-1/4 ,x= 1/3
Solve for x: x^{-2}+x^{-1}-12=0
The solution is x=-1/4 ,x= 1/3