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

The answer to 5/x =3-x/(x-3) is x=(7+sqrt(19))/2 ,x=(7-sqrt(19))/2

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

The solution is x=(7+sqrt(19))/2 ,x=(7-sqrt(19))/2

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

x = \frac{7 + 19}{2}, x = \frac{7 - 19}{2}

Decimal Notation

x = 5.67944 \dots, x = 1.32055 \dots

Solution steps

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

Multiply by LCM

5 (x - 3) = 3 x (x - 3) - x^{2}

Solve

5 (x - 3) = 3 x (x - 3) - x^{2} : x = \frac{7 + 19}{2}, x = \frac{7 - 19}{2}

x = \frac{7 + 19}{2}, x = \frac{7 - 19}{2}

Verify Solutions

Find undefined (singularity) points:

x = 0, x = 3

Combine undefined points with solutions:

x = \frac{7 + 19}{2}, x = \frac{7 - 19}{2}

\frac{5}{3 x} + 3 = 8

x^{- 2} + 3 x^{- 1} - 10 = 0

\frac{( x - 8 ) ^{2}}{x - 8} = 0

\frac{1}{x - 4} + \frac{1}{8} = 3

0.5854 = \frac{2.47 x}{1 + 1.47 x}

What is the answer to 5/x =3-x/(x-3) ?
The answer to 5/x =3-x/(x-3) is x=(7+sqrt(19))/2 ,x=(7-sqrt(19))/2
Solve for x: 5/x =3-x/(x-3)
The solution is x=(7+sqrt(19))/2 ,x=(7-sqrt(19))/2