What is (n^2}{n-1}-\frac{n+5)/n ?

The solution to (n^2}{n-1}-\frac{n+5)/n is (n^3-n^2-4n+5)/(n(n-1))

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simplify (n^2}{n-1}-\frac{n+5)/n

simplify

\frac{n ^{2}}{n - 1} - \frac{n + 5}{n}

\frac{n ^{3} - n ^{2} - 4 n + 5}{n ( n - 1 )}

Solution steps

\frac{n ^{2}}{n - 1} - \frac{n + 5}{n}

Least Common Multiplier of

n - 1, n : n (n - 1)

Adjust Fractions based on the LCM

= \frac{n ^{3}}{n ( n - 1 )} - \frac{( n + 5 ) ( n - 1 )}{n ( n - 1 )}

Apply the fraction rule:

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

= \frac{n ^{3} - ( n + 5 ) ( n - 1 )}{n ( n - 1 )}

Simplify

n^{3} - (n + 5) (n - 1) : n^{3} - n^{2} - 4 n + 5

= \frac{n ^{3} - n ^{2} - 4 n + 5}{n ( n - 1 )}

+ 5 - 4

+ 6 - 6

(x^{4} - 2)^{2}

1 1^{- 3}

- \frac{1}{3} \times 0

What is (n^2}{n-1}-\frac{n+5)/n ?
The solution to (n^2}{n-1}-\frac{n+5)/n is (n^3-n^2-4n+5)/(n(n-1))