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

The answer to 2=(2y)/(y+1)-3/(2y) is y=-3/7

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2=(2y)/(y+1)-3/(2y)

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

y = - \frac{3}{7}

Decimal Notation

y = - 0.42857 \dots

Solution steps

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

Multiply by LCM

4 y (y + 1) = 4 y^{2} - 3 (y + 1)

Expand

- 3 (y + 1) : - 3 y - 3

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

Expand

4 y (y + 1) : 4 y^{2} + 4 y

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

Subtract

4 y^{2} - 3 y

from both sides

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

Simplify

7 y = - 3

Divide both sides by

7

y = - \frac{3}{7}

Verify Solutions

Find undefined (singularity) points:

y = - 1, y = 0

Combine undefined points with solutions:

y = - \frac{3}{7}

\frac{6}{x ( 1 + 2 )} = 1

\frac{4 a}{x} + 6 = \frac{3 b}{x} + 2

\frac{5}{9 + 2 x} = \frac{3}{x}

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

\frac{4}{t} = \frac{5}{3}

What is the answer to 2=(2y)/(y+1)-3/(2y) ?
The answer to 2=(2y)/(y+1)-3/(2y) is y=-3/7
Solve for y: 2=(2y)/(y+1)-3/(2y)
The solution is y=-3/7