What is the answer to 1/x+1/(x-4)= 10/21 ?

The answer to 1/x+1/(x-4)= 10/21 is x=7,x= 6/5

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1/x+1/(x-4)= 10/21

\frac{1}{x} + \frac{1}{x - 4} = \frac{10}{21}

x = 7, x = \frac{6}{5}

Decimal Notation

x = 7, x = 1.2

Solution steps

\frac{1}{x} + \frac{1}{x - 4} = \frac{10}{21}

Multiply by LCM

21 (x - 4) + 21 x = 10 x (x - 4)

Solve

21 (x - 4) + 21 x = 10 x (x - 4) : x = 7, x = \frac{6}{5}

x = 7, x = \frac{6}{5}

Verify Solutions

Find undefined (singularity) points:

x = 0, x = 4

Combine undefined points with solutions:

x = 7, x = \frac{6}{5}

x - \frac{2 x}{x + 6} = \frac{5}{x + 6}

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

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

\frac{77770}{110 + x} = 708

\frac{6}{x + 5} = \frac{8}{x}

What is the answer to 1/x+1/(x-4)= 10/21 ?
The answer to 1/x+1/(x-4)= 10/21 is x=7,x= 6/5
Solve for x: 1/x+1/(x-4)= 10/21
The solution is x=7,x= 6/5