What is the answer to 2/y = 1/(y-2)-3 ?

The answer to 2/y = 1/(y-2)-3 is y=-(-5+sqrt(73))/6 ,y=(5+sqrt(73))/6

Solve for y: 2/y = 1/(y-2)-3

The solution is y=-(-5+sqrt(73))/6 ,y=(5+sqrt(73))/6

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\frac{2}{y} = \frac{1}{y - 2} - 3

y = - \frac{- 5 + 73}{6}, y = \frac{5 + 73}{6}

Decimal Notation

y = - 0.59066 \dots, y = 2.25733 \dots

Solution steps

\frac{2}{y} = \frac{1}{y - 2} - 3

Multiply by LCM

2 (y - 2) = y - 3 y (y - 2)

Solve

2 (y - 2) = y - 3 y (y - 2) : y = - \frac{- 5 + 73}{6}, y = \frac{5 + 73}{6}

y = - \frac{- 5 + 73}{6}, y = \frac{5 + 73}{6}

Verify Solutions

Find undefined (singularity) points:

y = 0, y = 2

Combine undefined points with solutions:

y = - \frac{- 5 + 73}{6}, y = \frac{5 + 73}{6}

y, x = \frac{y - 1}{y + 1}

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

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

1 - \frac{7}{x ^{2}} = 0

\frac{x - 3}{x} = \frac{3}{5}

What is the answer to 2/y = 1/(y-2)-3 ?
The answer to 2/y = 1/(y-2)-3 is y=-(-5+sqrt(73))/6 ,y=(5+sqrt(73))/6
Solve for y: 2/y = 1/(y-2)-3
The solution is y=-(-5+sqrt(73))/6 ,y=(5+sqrt(73))/6