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Question
Reduce the given Rational expression to its lowest form
`(10x^3 - 25x^2 + 4x - 10)/(-4 - 10x^2)`
Solution
10x3 – 25x2 + 4x – 10 = 5x2(2x – 5) + 2(2x – 5)
= (2x – 5) (5x2 + 2)
– 4 – 10x2 = – 2(2 + 5x2)
= – 2(5x2 + 2)
`(10x^3 - 25x^2 + 4x - 10)/(-4 - 10x^2) = ((2x - 5)(5x^2 + 2))/(-2(5x^2 + 2))`
= `(2x - 5)/(-2)` or `(2x)/(-2) - 5/(-2)`
= `- x + 5/2`
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