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

The answer to (3x)/(x-2)+1/x =4 is x=(9-sqrt(73))/2 ,x=(9+sqrt(73))/2

Solve for x: (3x)/(x-2)+1/x =4

The solution is x=(9-sqrt(73))/2 ,x=(9+sqrt(73))/2

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

x = \frac{9 - 73}{2}, x = \frac{9 + 73}{2}

Decimal Notation

x = 0.22799 \dots, x = 8.77200 \dots

Solution steps

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

Multiply by LCM

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

Solve

3 x^{2} + x - 2 = 4 x (x - 2) : x = \frac{9 - 73}{2}, x = \frac{9 + 73}{2}

x = \frac{9 - 73}{2}, x = \frac{9 + 73}{2}

Verify Solutions

Find undefined (singularity) points:

x = 2, x = 0

Combine undefined points with solutions:

x = \frac{9 - 73}{2}, x = \frac{9 + 73}{2}

\frac{2}{x} = \frac{4}{5 x} + 2

\frac{x ^{3}}{2 x ^{5}} = 2

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

0 = \frac{x + 3}{2 x ^{2} - 6}

\frac{( x + 5 ) ^{2} - 4}{x + 3} = 0

What is the answer to (3x)/(x-2)+1/x =4 ?
The answer to (3x)/(x-2)+1/x =4 is x=(9-sqrt(73))/2 ,x=(9+sqrt(73))/2
Solve for x: (3x)/(x-2)+1/x =4
The solution is x=(9-sqrt(73))/2 ,x=(9+sqrt(73))/2