when you get to this point:
70x^2/x - 51x /x - 70/x < 0
multiply by x to get
70x^2 - 51x - 70 < 0 and note that x≠0
since 1/x is not defined for x=0
now you have
(10x+7)(7x-10) < 0
At this point you should have some idea what you are looking for. You know it is a parabola which opens upward, and crosses the x-axis at -7/10 and 10/7.
So, the interval between the roots satisfies the original inequality:
-7/10 < x < 10/7
(10x+7)(7x-10) < 0, either
(10x+7) < 0 and (7x-10) > 0
(10x+7) > 0 and (7x-10) < 0
solve those and you will find a solution set which agrees to the interval above.
oops. because x cannot be 0, the final solution is
(-7/10,0) U (0,10/7)
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