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

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

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(x^2+2)/x =x+2

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

x = 1

Solution steps

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

Multiply both sides by

x

x^{2} + 2 = x^{2} + 2 x

Subtract

x^{2}

from both sides

x^{2} + 2 - x^{2} = x^{2} + 2 x - x^{2}

Simplify

2 = 2 x

Switch sides

2 x = 2

Divide both sides by

2

x = 1

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = 1

x^{- 2} + 2 x^{- 1} - 24 = 0

\frac{2}{3 m + 2} = 0

\frac{n - 9}{n + 5} = \frac{7}{4}

\frac{11}{2} = \frac{22}{x}

x^{- 2} = 25