What is the answer to x(5x-3-2/x)=0 ?

The answer to x(5x-3-2/x)=0 is x=1,x=-2/5

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x(5x-3-2/x)=0

x (5 x - 3 - \frac{2}{x}) = 0

x = 1, x = - \frac{2}{5}

Solution steps

x (5 x - 3 - \frac{2}{x}) = 0

Simplify

x (5 x - 3 - \frac{2}{x}) : 5 x^{2} - 3 x - 2

5 x^{2} - 3 x - 2 = 0

Solve

5 x^{2} - 3 x - 2 = 0 : x = 1, x = - \frac{2}{5}

x = 1, x = - \frac{2}{5}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = 1, x = - \frac{2}{5}

\frac{x}{x - 2} = \frac{2}{x - 2} + 3

2 = \frac{5}{x}

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

\frac{8}{x + 3} + \frac{3}{x + 8} = 1

16 = \frac{1}{x ^{2}}