What is the answer to (20x)/(4x-1)+2/x =5 ?

The answer to (20x)/(4x-1)+2/x =5 is x= 2/13

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(20x)/(4x-1)+2/x =5

\frac{20 x}{4 x - 1} + \frac{2}{x} = 5

x = \frac{2}{13}

Decimal Notation

x = 0.15384 \dots

Solution steps

\frac{20 x}{4 x - 1} + \frac{2}{x} = 5

Multiply by LCM

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

Expand

2 (4 x - 1) : 8 x - 2

20 x^{2} + 8 x - 2 = 5 x (4 x - 1)

Expand

5 x (4 x - 1) : 20 x^{2} - 5 x

20 x^{2} + 8 x - 2 = 20 x^{2} - 5 x

Move

2

to the right side

20 x^{2} + 8 x = 20 x^{2} - 5 x + 2

Subtract

20 x^{2} - 5 x

from both sides

20 x^{2} + 8 x - (20 x^{2} - 5 x) = 20 x^{2} - 5 x + 2 - (20 x^{2} - 5 x)

Simplify

13 x = 2

Divide both sides by

13

x = \frac{2}{13}

Verify Solutions

Find undefined (singularity) points:

x = \frac{1}{4}, x = 0

Combine undefined points with solutions:

x = \frac{2}{13}

\frac{12}{( y + 4 )} = 1

N = 50000 - \frac{2000}{t + 1}

4 (x + 3) - 4 = 8 (\frac{1}{2 x + 1})

\frac{9}{g} = \frac{15}{10}

\frac{3}{r} + \frac{5}{3 r} = 1

What is the answer to (20x)/(4x-1)+2/x =5 ?
The answer to (20x)/(4x-1)+2/x =5 is x= 2/13
Solve for x: (20x)/(4x-1)+2/x =5
The solution is x= 2/13