What is the answer to (3y)/(y-4)=3+2/y ?

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

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(3y)/(y-4)=3+2/y

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

y = - \frac{4}{5}

Decimal Notation

y = - 0.8

Solution steps

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

Multiply by LCM

3 y^{2} = 3 y (y - 4) + 2 (y - 4)

Expand

3 y (y - 4) : 3 y^{2} - 12 y

3 y^{2} = 3 y^{2} - 12 y + 2 (y - 4)

Expand

2 (y - 4) : 2 y - 8

3 y^{2} = 3 y^{2} - 12 y + 2 y - 8

Add similar elements:

- 12 y + 2 y = - 10 y

3 y^{2} = 3 y^{2} - 10 y - 8

Subtract

3 y^{2} - 10 y

from both sides

3 y^{2} - (3 y^{2} - 10 y) = 3 y^{2} - 10 y - 8 - (3 y^{2} - 10 y)

Simplify

10 y = - 8

Divide both sides by

10

y = - \frac{4}{5}

Verify Solutions

Find undefined (singularity) points:

y = 4, y = 0

Combine undefined points with solutions:

y = - \frac{4}{5}

2 = \frac{5}{r - 5}

80 = \frac{x ^{2} + 300 x}{2 x + 300}

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

\frac{4}{x - 1} - \frac{3 - x}{2} = 2

6817 = \frac{( x + 2 )}{( x + 4.47 )}

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