What is the answer to (4x)/(x-1)+1/x =5 ?

The answer to (4x)/(x-1)+1/x =5 is x=3-2sqrt(2),x=3+2sqrt(2)

Solve for x: (4x)/(x-1)+1/x =5

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

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\frac{4 x}{x - 1} + \frac{1}{x} = 5

x = 3 - 22, x = 3 + 22

Decimal Notation

x = 0.17157 \dots, x = 5.82842 \dots

Solution steps

\frac{4 x}{x - 1} + \frac{1}{x} = 5

Multiply by LCM

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

Solve

4 x^{2} + x - 1 = 5 x (x - 1) : x = 3 - 22, x = 3 + 22

x = 3 - 22, x = 3 + 22

Verify Solutions

Find undefined (singularity) points:

x = 1, x = 0

Combine undefined points with solutions:

x = 3 - 22, x = 3 + 22

160 = \frac{180 ( n - 2 )}{n}

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

x + \frac{475}{x} = 25

\frac{100 x}{1 + x} = 50

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

What is the answer to (4x)/(x-1)+1/x =5 ?
The answer to (4x)/(x-1)+1/x =5 is x=3-2sqrt(2),x=3+2sqrt(2)
Solve for x: (4x)/(x-1)+1/x =5
The solution is x=3-2sqrt(2),x=3+2sqrt(2)