7-5). Reduce the following rational expression to lowest terms, if possible. 2x^2+5x-12 ____________ x^4-256

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7-5). Reduce the following rational expression to lowest terms, if possible. 2x^2+5x-12 ____________ x^4-256

Mathematics
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Try to factorise top and bottom. Top factorises as (2x - 3)(x + 4). Do you know how to factorise a non-monic quadratic expression? The bottom looks like the difference of two squares: x^2 squared and 16 squared So bottom is (x^2 +16)(x^2 - 16), but second bracket is again the difference between two squares So bottom line is (x^2 + 16)(x - 4)(x + 4) We can cancel top and bottom (x + 4) to give us: (2x - 3)/(x^2 + 16)(x - 4)

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