Question

Reduce the given Rational expressions to its lowest form (i) (x^3a - 8)/(x^2a + 2x^a + 4) (ii) (10x³ - 25x² + 4x - 10)/(-4 - 10x² )

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Answer 1

(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 = x^a and b = 2)

= x^a - 2

(ii) \(\frac{10x^3-25x^2+4x-10}{-4-10x^2}\)

\(=\frac{5x^2(2x-5)+2(2x-5)}{-2(2+5x^2)}\)

\(=\frac{(2x-5)(2+5x^2)}{-2(2+5x^2)}\)

\(= \frac{2x-5}{-2}\)

\(=\frac{5-2x}{2}\)