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

The answer to 1/x+1/(x-1)=3 is x=(5+sqrt(13))/6 ,x=(5-sqrt(13))/6

Solve for x: 1/x+1/(x-1)=3

The solution is x=(5+sqrt(13))/6 ,x=(5-sqrt(13))/6

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

x = \frac{5 + 13}{6}, x = \frac{5 - 13}{6}

Decimal Notation

x = 1.43425 \dots, x = 0.23240 \dots

Solution steps

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

Multiply by LCM

2 x - 1 = 3 x (x - 1)

Solve

2 x - 1 = 3 x (x - 1) : x = \frac{5 + 13}{6}, x = \frac{5 - 13}{6}

x = \frac{5 + 13}{6}, x = \frac{5 - 13}{6}

Verify Solutions

Find undefined (singularity) points:

x = 0, x = 1

Combine undefined points with solutions:

x = \frac{5 + 13}{6}, x = \frac{5 - 13}{6}

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

0 = \frac{2 x + 1}{x + 1}

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

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

\frac{x ^{2} + 6 x + 9}{x + 3} = 0

What is the answer to 1/x+1/(x-1)=3 ?
The answer to 1/x+1/(x-1)=3 is x=(5+sqrt(13))/6 ,x=(5-sqrt(13))/6
Solve for x: 1/x+1/(x-1)=3
The solution is x=(5+sqrt(13))/6 ,x=(5-sqrt(13))/6