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

The answer to (x-4)/x+(x^{-1})/3 =-2 is x= 11/9

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(x-4)/x+(x^{-1})/3 =-2

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

x = \frac{11}{9}

Decimal Notation

x = 1.22222 \dots

Solution steps

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

Refine

\frac{x - 4}{x} + \frac{1}{3 x} = - 2

Multiply by LCM

3 x - 11 = - 6 x

Move

11

to the right side

3 x = - 6 x + 11

Move

6 x

to the left side

9 x = 11

Divide both sides by

9

x = \frac{11}{9}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = \frac{11}{9}

\frac{2}{x} = \frac{8}{32}

- \frac{8}{y + 8} = - 5

x^{3} + \frac{27}{x ^{3}} = 28

\frac{1}{( x - 1 ) ^{2}} + \frac{3}{x - 1} - 10 = 0

0.1 = \frac{1}{\frac{1}{2} t + 1}

What is the answer to (x-4)/x+(x^{-1})/3 =-2 ?
The answer to (x-4)/x+(x^{-1})/3 =-2 is x= 11/9
Solve for x: (x-4)/x+(x^{-1})/3 =-2
The solution is x= 11/9