What is the answer to 3/(x+2)-1/x = 1/(5x) ?

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

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3/(x+2)-1/x = 1/(5x)

\frac{3}{x + 2} - \frac{1}{x} = \frac{1}{5 x}

x = \frac{4}{3}

Decimal Notation

x = 1.33333 \dots

Solution steps

\frac{3}{x + 2} - \frac{1}{x} = \frac{1}{5 x}

Multiply by LCM

15 x - 5 (x + 2) = x + 2

Expand

- 5 (x + 2) : - 5 x - 10

15 x - 5 x - 10 = x + 2

Add similar elements:

15 x - 5 x = 10 x

10 x - 10 = x + 2

Move

10

to the right side

10 x = x + 12

Move

x

to the left side

9 x = 12

Divide both sides by

9

x = \frac{4}{3}

Verify Solutions

Find undefined (singularity) points:

x = - 2, x = 0

Combine undefined points with solutions:

x = \frac{4}{3}

\frac{11}{x - 9} = - 10

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

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

\frac{20}{x ^{2} - 4 x + 7} = x + 2

\frac{1}{x} - \frac{x}{6} = \frac{2}{3}

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