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

The answer to x+1/x = 5/2 is x=2,x= 1/2

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x+1/x = 5/2

x + \frac{1}{x} = \frac{5}{2}

x = 2, x = \frac{1}{2}

Solution steps

x + \frac{1}{x} = \frac{5}{2}

Multiply by LCM

2 x^{2} + 2 = 5 x

Solve

2 x^{2} + 2 = 5 x : x = 2, x = \frac{1}{2}

x = 2, x = \frac{1}{2}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = 2, x = \frac{1}{2}

\frac{8}{6} = \frac{4}{x - 7}

\frac{3 y - 1}{2 y + 4} = \frac{4}{5}

\frac{2 x}{1 + x ^{2}} = 0

\frac{6}{3 c} = \frac{2}{3}

\frac{∣ x - 2 ∣}{x - 2} = 1