What is the solution of the fraction with numerator x plus 8 and denominator 5 x minus 1 is greater than 0 ?

The fraction can change sign at x = -8, where the numerator is zero, and x = 1/5, where the denominator is zero. Testing the intervals shows the fraction is positive when x < -8 or x > 1/5. Both endpoints are excluded because the inequality is strict, and the denominator cannot be zero. Therefore, the solution is “x is less than negative 8 or x is greater than 1 fifth.”

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