What is the answer to ((x-1/3)^2+2)/(3*x)= 10/9 ?

The answer to ((x-1/3)^2+2)/(3*x)= 10/9 is x=(6+sqrt(17))/3 ,x=(6-sqrt(17))/3

Solve for x: ((x-1/3)^2+2)/(3*x)= 10/9

The solution is x=(6+sqrt(17))/3 ,x=(6-sqrt(17))/3

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\frac{( x - \frac{1}{3} ) ^{2} + 2}{3 \cdot x} = \frac{10}{9}

x = \frac{6 + 17}{3}, x = \frac{6 - 17}{3}

Decimal Notation

x = 3.37436 \dots, x = 0.62563 \dots

Solution steps

\frac{( x - \frac{1}{3} ) ^{2} + 2}{3 x} = \frac{10}{9}

Cross multiply

(19 - 6 x + 9 x^{2}) \cdot 9 = 270 x

Solve

(19 - 6 x + 9 x^{2}) \cdot 9 = 270 x : x = \frac{6 + 17}{3}, x = \frac{6 - 17}{3}

x = \frac{6 + 17}{3}, x = \frac{6 - 17}{3}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = \frac{6 + 17}{3}, x = \frac{6 - 17}{3}

\frac{( x ^{2} - 6 )}{x} - \frac{( 3 x )}{( x ^{2} - 6 )} = - 2

\frac{( 3 x + 7 )}{( x + 2 ) + x} = \frac{1}{( x + 2 ) + 8}

\frac{( x + 1 )}{3} = \frac{21}{2 + 2 x - 1}

a, (a + b)^{- 1} = a^{- 1} + b^{- 1}

\frac{4}{x ^{2}} = \frac{1}{( a - x ) 2}

What is the answer to ((x-1/3)^2+2)/(3*x)= 10/9 ?
The answer to ((x-1/3)^2+2)/(3*x)= 10/9 is x=(6+sqrt(17))/3 ,x=(6-sqrt(17))/3
Solve for x: ((x-1/3)^2+2)/(3*x)= 10/9
The solution is x=(6+sqrt(17))/3 ,x=(6-sqrt(17))/3