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Find the values of x for which the inequality 8x2 + 16x - 51/(2x - 3)(x + 4)> holds.

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We cannot write 8x2 + 16x − 51 > 3 (2x − 3) (x + 4) as this would be correct only if (2x − 3) (x + 4) is positive.

Therefore, transfer 3 to L.H.S. and rewrite as

Multiplying both sides by the square of the denominator, we get

Therefore, the inequality has the solution

 

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