What is the answer to 2(x-5)^{-1}+1/x =0 ?

The answer to 2(x-5)^{-1}+1/x =0 is x= 5/3

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2(x-5)^{-1}+1/x =0

2 (x - 5)^{- 1} + \frac{1}{x} = 0

x = \frac{5}{3}

Decimal Notation

x = 1.66666 \dots

Solution steps

2 (x - 5)^{- 1} + \frac{1}{x} = 0

Refine

\frac{2}{x - 5} + \frac{1}{x} = 0

Multiply by LCM

3 x - 5 = 0

Move

5

to the right side

3 x = 5

Divide both sides by

3

x = \frac{5}{3}

Verify Solutions

Find undefined (singularity) points:

x = 5, x = 0

Combine undefined points with solutions:

x = \frac{5}{3}

\frac{3}{m - 1} = \frac{6}{3 m + 8}

\frac{2 x}{x + 9} = \frac{2 x - 9}{x}

y, x = \frac{y}{y + 1}

\frac{6 x + 24}{x + 4} = 5

\frac{1}{2 x - 1} = \frac{4}{8 x - 4}

What is the answer to 2(x-5)^{-1}+1/x =0 ?
The answer to 2(x-5)^{-1}+1/x =0 is x= 5/3
Solve for x: 2(x-5)^{-1}+1/x =0
The solution is x= 5/3