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Solution 2.1:6b

From Förberedande kurs i matematik 1

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The lowest common denominator for the three terms is x2x+3  and we expand each term so that all terms have the same denominator:


xx2+xx+32=xx2x+3x+3+xx+3x2x22x2x+3x2x+3=x2x+3xx+3+xx22x2x+3=x2x+3x2+3x+x22x2x2+3x2x6=x2x+3x2+3x+x22x2x26x+4x+12


Now, collect together the terms in the numerator:


xx2+xx+32=x2x+3x2+x22x2+3x2x6x+4x+12=x+12x2x+3


NOTE: By keeping the denominator factorized during the entire calculation, we can see at the end that the answer cannot be simplified any further.