What is the answer to x/((x^2+1))+((x^2+1))/x = 5/2 ?

The answer to x/((x^2+1))+((x^2+1))/x = 5/2 is x=1,x= 1/4+i(sqrt(15))/4 ,x= 1/4-i(sqrt(15))/4

Solve for x: x/((x^2+1))+((x^2+1))/x = 5/2

The solution is x=1,x= 1/4+i(sqrt(15))/4 ,x= 1/4-i(sqrt(15))/4

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\frac{x}{( x ^{2} + 1 )} + \frac{( x ^{2} + 1 )}{x} = \frac{5}{2}

x = 1, x = \frac{1}{4} + i \frac{15}{4}, x = \frac{1}{4} - i \frac{15}{4}

Solution steps

\frac{x}{( x ^{2} + 1 )} + \frac{( x ^{2} + 1 )}{x} = \frac{5}{2}

Multiply by LCM

2 x^{2} + 2 (x^{2} + 1)^{2} = 5 x (x^{2} + 1)

Solve

2 x^{2} + 2 (x^{2} + 1)^{2} = 5 x (x^{2} + 1) : x = 1, x = \frac{1}{4} + i \frac{15}{4}, x = \frac{1}{4} - i \frac{15}{4}

x = 1, x = \frac{1}{4} + i \frac{15}{4}, x = \frac{1}{4} - i \frac{15}{4}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = 1, x = \frac{1}{4} + i \frac{15}{4}, x = \frac{1}{4} - i \frac{15}{4}

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

\frac{2}{( x - 3 )} + \frac{1}{( x - 1 )} = \frac{5}{( x - 1 )} - \frac{2}{( x - 2 )}

\frac{1}{7 \cdot x ^{2} + 1} = \frac{4}{7 \cdot x}

x, 3 y = \frac{( 7 w )}{x}

\frac{7 x - 3 + 32}{3 \cdot x - 1} = \frac{1}{3}

What is the answer to x/((x^2+1))+((x^2+1))/x = 5/2 ?
The answer to x/((x^2+1))+((x^2+1))/x = 5/2 is x=1,x= 1/4+i(sqrt(15))/4 ,x= 1/4-i(sqrt(15))/4
Solve for x: x/((x^2+1))+((x^2+1))/x = 5/2
The solution is x=1,x= 1/4+i(sqrt(15))/4 ,x= 1/4-i(sqrt(15))/4