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

The answer to (2x)/(x-2)+1/x =3 is x=(7-sqrt(41))/2 ,x=(7+sqrt(41))/2

Solve for x: (2x)/(x-2)+1/x =3

The solution is x=(7-sqrt(41))/2 ,x=(7+sqrt(41))/2

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

x = \frac{7 - 41}{2}, x = \frac{7 + 41}{2}

Decimal Notation

x = 0.29843 \dots, x = 6.70156 \dots

Solution steps

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

Multiply by LCM

2 x^{2} + x - 2 = 3 x (x - 2)

Solve

2 x^{2} + x - 2 = 3 x (x - 2) : x = \frac{7 - 41}{2}, x = \frac{7 + 41}{2}

x = \frac{7 - 41}{2}, x = \frac{7 + 41}{2}

Verify Solutions

Find undefined (singularity) points:

x = 2, x = 0

Combine undefined points with solutions:

x = \frac{7 - 41}{2}, x = \frac{7 + 41}{2}

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

\frac{2 x}{x - 3} = \frac{6}{x - 3} + 4

\frac{3}{x + 4} - 7 = - \frac{4}{x + 4}

x^{- 2} = 100

\frac{2}{0.21} = \frac{8}{n}

What is the answer to (2x)/(x-2)+1/x =3 ?
The answer to (2x)/(x-2)+1/x =3 is x=(7-sqrt(41))/2 ,x=(7+sqrt(41))/2
Solve for x: (2x)/(x-2)+1/x =3
The solution is x=(7-sqrt(41))/2 ,x=(7+sqrt(41))/2