What is the answer to x^{-2}+4x^{-1}+3=0 ?

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

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x^{-2}+4x^{-1}+3=0

x^{- 2} + 4 x^{- 1} + 3 = 0

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

Decimal Notation

x = - 0.33333 \dots, x = - 1

Solution steps

x^{- 2} + 4 x^{- 1} + 3 = 0

Refine

\frac{1}{x ^{2}} + \frac{4}{x} + 3 = 0

Multiply by LCM

1 + 4 x + 3 x^{2} = 0

Solve

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

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

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

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

\frac{2}{3} = \frac{8}{x}

\frac{6}{2 m + 7} = \frac{10}{3 m - 8}

\frac{10}{x + 18} = \frac{x + 1}{6}

4 + \frac{3}{x + 1} = \frac{3}{5}

\frac{x ^{2}}{x + 20} = 10

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