What is 1/((n-1)^2)+1/(n-1)-1/((n-1)^3)-1/n ?

The solution to 1/((n-1)^2)+1/(n-1)-1/((n-1)^3)-1/n is (2n^2-4n+1)/(n(n-1)^3)

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simplify 1/((n-1)^2)+1/(n-1)-1/((n-1)^3)-1/n

simplify

\frac{1}{( n - 1 ) ^{2}} + \frac{1}{n - 1} - \frac{1}{( n - 1 ) ^{3}} - \frac{1}{n}

\frac{2 n ^{2} - 4 n + 1}{n ( n - 1 ) ^{3}}

Solution steps

\frac{1}{( n - 1 ) ^{2}} + \frac{1}{n - 1} - \frac{1}{( n - 1 ) ^{3}} - \frac{1}{n}

Least Common Multiplier of

(n - 1)^{2}, n - 1, (n - 1)^{3}, n : n (n - 1)^{3}

Adjust Fractions based on the LCM

= \frac{n ( n - 1 )}{n ( n - 1 ) ^{3}} + \frac{n ( n - 1 ) ^{2}}{n ( n - 1 ) ^{3}} - \frac{n}{n ( n - 1 ) ^{3}} - \frac{( n - 1 ) ^{3}}{n ( n - 1 ) ^{3}}

Apply the fraction rule:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{n ( n - 1 ) + n ( n - 1 ) ^{2} - n - ( n - 1 ) ^{3}}{n ( n - 1 ) ^{3}}

Simplify

n (n - 1) + n (n - 1)^{2} - n - (n - 1)^{3} : 2 n^{2} - 4 n + 1

= \frac{2 n ^{2} - 4 n + 1}{n ( n - 1 ) ^{3}}

2 \cdot 8

[4 w + 2] - 6 > 8

2 (- 3)^{3} + 2

2 x - 3 > 7

\frac{1}{x + 1} > 3

What is 1/((n-1)^2)+1/(n-1)-1/((n-1)^3)-1/n ?
The solution to 1/((n-1)^2)+1/(n-1)-1/((n-1)^3)-1/n is (2n^2-4n+1)/(n(n-1)^3)