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Reduce the given Rational expressions to its lowest form (i) (x3a - 8)/(x2a + 2xa + 4) (ii) (10x3 - 25x2 + 4x - 10)/(-4 - 10x2 ) |
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Answer» (i) \(\frac{x^{3a}-8}{x^{2a}+2x^a+4}=\frac{(x^a)^3-2^3}{x^{2a}+2x^a+4}\) \(=\frac {(x^a-2)(x^{2a}+2x^a+4)}{x^{2a}+2x^a+4}\) (∵ a3 - b3 = (a - b)(a2 + ab + b2) and here a = xa and b = 2) = xa - 2 (ii) \(\frac{10x^3-25x^2+4x-10}{-4-10x^2}\) \(=\frac{5x^2(2x-5)+2(2x-5)}{-2(2+5x^2)}\) \(=\frac{(2x-5)(2+5x^2)}{-2(2+5x^2)}\) \(= \frac{2x-5}{-2}\) \(=\frac{5-2x}{2}\) |
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