What is the answer to (5x^2+1)/x =6 ?

The answer to (5x^2+1)/x =6 is x=1,x= 1/5

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(5x^2+1)/x =6

\frac{5 x ^{2} + 1}{x} = 6

x = 1, x = \frac{1}{5}

Decimal Notation

x = 1, x = 0.2

Solution steps

\frac{5 x ^{2} + 1}{x} = 6

Multiply both sides by

x

5 x^{2} + 1 = 6 x

Solve

5 x^{2} + 1 = 6 x : x = 1, x = \frac{1}{5}

x = 1, x = \frac{1}{5}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = 1, x = \frac{1}{5}

\frac{( x ^{2} + 5 x + 6 )}{( x + 3 )} = x + 7

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

x^{- 3} = 8

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

(\frac{x}{( x - 1 )})^{2} + 4 (\frac{x}{( x - 1 )}) + 2 = 0