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Question
Reduce the given Rational expression to its lowest form
`(x^(3"a") - 8)/(x^(2"a") + 2x^"a" + 4)`
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Solution
x3a – 8 = (xa)3 – 23 ...(using the formula a3 – b3 = (a – b)(a2 + ab + b2)
= (xa – 2)[(xa)2 + xa × 2 + 22]
= (xa – 2) (x2a + 2xa + 4)
`(x^(3"a") - 8)/(x^(2"a") + 2x^"a" + 4) = ((x^"a" - 2)(x^(2"a") + 2x^"a" + 4))/((x^(2"a") + 2x^"a" + 4))`
= xa – 2
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