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Solution 2.1:7c

From Förberedande kurs i matematik 1

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We multiply the top and bottom of the first term by a+1, so that both terms then have the same denominator,

axa+1a+1a+1−ax2(a+1)2=(a+1)2ax(a+1)−ax2.

Because both terms in the numerator contain the factor ax, we take out that factor, obtaining

(a+1)2ax(a+1−x)

and see that the answer cannot be simplified any further.

Note: It is only factors in the numerator and denominator that can cancel each other out, not individual terms. Hence, the following "cancellation" is wrong

(a+1)2ax(a+1)−ax2=a+1ax−ax2.
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