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

The answer to 3/x =5-(2+3x)/(x-3) is x=(10+sqrt(82))/2 ,x=(10-sqrt(82))/2

Solve for x: 3/x =5-(2+3x)/(x-3)

The solution is x=(10+sqrt(82))/2 ,x=(10-sqrt(82))/2

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

x = \frac{10 + 82}{2}, x = \frac{10 - 82}{2}

Decimal Notation

x = 9.52769 \dots, x = 0.47230 \dots

Solution steps

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

Multiply by LCM

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

Solve

3 (x - 3) = 5 x (x - 3) - x (2 + 3 x) : x = \frac{10 + 82}{2}, x = \frac{10 - 82}{2}

x = \frac{10 + 82}{2}, x = \frac{10 - 82}{2}

Verify Solutions

Find undefined (singularity) points:

x = 0, x = 3

Combine undefined points with solutions:

x = \frac{10 + 82}{2}, x = \frac{10 - 82}{2}

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

y + \frac{7}{2} = \frac{2}{y}

\frac{10}{x} = 20

- \frac{1 - s}{( 1 - s ) ^{2} + 1} = 0

\frac{24}{32} = \frac{15}{x}

What is the answer to 3/x =5-(2+3x)/(x-3) ?
The answer to 3/x =5-(2+3x)/(x-3) is x=(10+sqrt(82))/2 ,x=(10-sqrt(82))/2
Solve for x: 3/x =5-(2+3x)/(x-3)
The solution is x=(10+sqrt(82))/2 ,x=(10-sqrt(82))/2