What is the answer to 4/(y-1)-5/(y+2)= 3/y ?

The answer to 4/(y-1)-5/(y+2)= 3/y is y=3,y=-1/2

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4/(y-1)-5/(y+2)= 3/y

\frac{4}{y - 1} - \frac{5}{y + 2} = \frac{3}{y}

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

Decimal Notation

y = 3, y = - 0.5

Solution steps

\frac{4}{y - 1} - \frac{5}{y + 2} = \frac{3}{y}

Multiply by LCM

4 y (y + 2) - 5 y (y - 1) = 3 (y - 1) (y + 2)

Solve

4 y (y + 2) - 5 y (y - 1) = 3 (y - 1) (y + 2) : y = 3, y = - \frac{1}{2}

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

Verify Solutions

Find undefined (singularity) points:

y = - 2, y = 1, y = 0

Combine undefined points with solutions:

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

2 - \frac{98}{x ^{2}} = 0

\frac{1}{15} = \frac{1}{20} + \frac{1}{x}

\frac{1}{m} = \frac{m - 34}{2 m ^{2}}

2 - \frac{6}{x ^{2}} = 0

\frac{1}{x} - \frac{1}{x + 3} = \frac{3}{10}

What is the answer to 4/(y-1)-5/(y+2)= 3/y ?
The answer to 4/(y-1)-5/(y+2)= 3/y is y=3,y=-1/2
Solve for y: 4/(y-1)-5/(y+2)= 3/y
The solution is y=3,y=-1/2