What is the answer to 5/(2x)=3-2/x ?

The answer to 5/(2x)=3-2/x is x= 3/2

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5/(2x)=3-2/x

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

x = \frac{3}{2}

Decimal

x = 1.5

Solution steps

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

Multiply by LCM

5 = 6 x - 4

Switch sides

6 x - 4 = 5

Move

4

to the right side

6 x = 9

Divide both sides by

6

x = \frac{3}{2}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = \frac{3}{2}

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

x^{2} + \frac{x ^{2}}{( x + 1 ) ^{2}} = 3

6 = 9 - 90000 (\frac{1}{10000 + 3 t})

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

\frac{5}{x ^{2}} - \frac{54}{x} = 11