An algebra problem by Aareyan Manzoor

Algebra Level 3

which of these are equal to 1n2(n+1)+1n(n+1)2 \frac{1}{n^2(n+1)}+\frac{1}{n(n+1)^2}

i) 1n2(n1)2+2n(n1)2 \frac{1}{n^2(n-1)^2}+\frac{2}{n(n-1)^2}
ii) 1n2(n+1)2+2n(n+1)2\frac{1}{n^2(n+1)^2}+\frac{2}{n(n+1)^2}
iii) 1n2)1n+1)2\frac{1}{n^2)}-\frac{1}{n+1)^2}
Iv)(1n+1+1n)(1n1n+1) (\frac {1}{n+1} +\frac{1}{n})(\frac{1}{n}-\frac{1}{n+1})

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