What is the answer to 4/Y =(18)/(3Y)+1 ?

The answer to 4/Y =(18)/(3Y)+1 is Y=-2

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4/Y =(18)/(3Y)+1

\frac{4}{Y} = \frac{18}{3 Y} + 1

Y = - 2

Solution steps

\frac{4}{Y} = \frac{18}{3 Y} + 1

Simplify

\frac{18}{3 Y} : \frac{6}{Y}

\frac{4}{Y} = \frac{6}{Y} + 1

Multiply both sides by

Y

4 = 6 + Y

Switch sides

6 + Y = 4

Move

6

to the right side

Y = - 2

Verify Solutions

Find undefined (singularity) points:

Y = 0

Combine undefined points with solutions:

Y = - 2

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

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

\frac{4}{3 x} + \frac{5}{4} = \frac{3}{x}

x^{- 2} - 2 x^{- 1} - 15 = 0

2 x - \frac{54}{x ^{2}} = 0