What is the answer to (4x)/(x-2)+2/x =5 ?

The answer to (4x)/(x-2)+2/x =5 is x=2(3-2sqrt(2)),x=2(3+2sqrt(2))

Solve for x: (4x)/(x-2)+2/x =5

The solution is x=2(3-2sqrt(2)),x=2(3+2sqrt(2))

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

x = 2 (3 - 22), x = 2 (3 + 22)

Decimal Notation

x = 0.34314 \dots, x = 11.65685 \dots

Solution steps

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

Multiply by LCM

4 x^{2} + 2 (x - 2) = 5 x (x - 2)

Solve

4 x^{2} + 2 (x - 2) = 5 x (x - 2) : x = 2 (3 - 22), x = 2 (3 + 22)

x = 2 (3 - 22), x = 2 (3 + 22)

Verify Solutions

Find undefined (singularity) points:

x = 2, x = 0

Combine undefined points with solutions:

x = 2 (3 - 22), x = 2 (3 + 22)

\frac{1}{x} = - 1

x - 3 = \frac{10}{x}

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

\frac{x}{x - 3} + 5 = \frac{3}{x - 3}

\frac{x - 9}{x - 6} = \frac{- 4}{x}

What is the answer to (4x)/(x-2)+2/x =5 ?
The answer to (4x)/(x-2)+2/x =5 is x=2(3-2sqrt(2)),x=2(3+2sqrt(2))
Solve for x: (4x)/(x-2)+2/x =5
The solution is x=2(3-2sqrt(2)),x=2(3+2sqrt(2))