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

The answer to (2x)/(x-3)+2/x =3 is x=(11-sqrt(97))/2 ,x=(11+sqrt(97))/2

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

The solution is x=(11-sqrt(97))/2 ,x=(11+sqrt(97))/2

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

x = \frac{11 - 97}{2}, x = \frac{11 + 97}{2}

Decimal Notation

x = 0.57557 \dots, x = 10.42442 \dots

Solution steps

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

Multiply by LCM

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

Solve

2 x^{2} + 2 (x - 3) = 3 x (x - 3) : x = \frac{11 - 97}{2}, x = \frac{11 + 97}{2}

x = \frac{11 - 97}{2}, x = \frac{11 + 97}{2}

Verify Solutions

Find undefined (singularity) points:

x = 3, x = 0

Combine undefined points with solutions:

x = \frac{11 - 97}{2}, x = \frac{11 + 97}{2}

\frac{7}{4 x - 1} = \frac{2}{x + 3}

\frac{2 x - 1}{( x + 2 ) ( x ^{2} + 3 )} = 0

- 1.45 = \frac{948 - 956}{x}

15 - \frac{1}{6 n} = \frac{1}{6 n} - 1

\frac{6}{- x} = \frac{2 x}{- 3}

What is the answer to (2x)/(x-3)+2/x =3 ?
The answer to (2x)/(x-3)+2/x =3 is x=(11-sqrt(97))/2 ,x=(11+sqrt(97))/2
Solve for x: (2x)/(x-3)+2/x =3
The solution is x=(11-sqrt(97))/2 ,x=(11+sqrt(97))/2