What is n/(n+1)+1/((n+1)(n+2)) ?

The solution to n/(n+1)+1/((n+1)(n+2)) is (n+1)/(n+2)

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simplify n/(n+1)+1/((n+1)(n+2))

simplify

\frac{n}{n + 1} + \frac{1}{( n + 1 ) ( n + 2 )}

\frac{n + 1}{n + 2}

Solution steps

\frac{n}{n + 1} + \frac{1}{( n + 1 ) ( n + 2 )}

Least Common Multiplier of

n + 1, (n + 1) (n + 2) : (n + 1) (n + 2)

Adjust Fractions based on the LCM

= \frac{n ( n + 2 )}{( n + 1 ) ( n + 2 )} + \frac{1}{( n + 1 ) ( n + 2 )}

Apply the fraction rule:

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

= \frac{n ( n + 2 ) + 1}{( n + 1 ) ( n + 2 )}

Simplify

n (n + 2) + 1 : n^{2} + 2 n + 1

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

Cancel

\frac{n ^{2} + 2 n + 1}{( n + 1 ) ( n + 2 )} : \frac{n + 1}{n + 2}

= \frac{n + 1}{n + 2}

x^{3} - 3 x^{2} + x - 3

121

\frac{6 x ^{2}}{( \frac{4 x}{y} \frac{3 y ^{2}}{2} )}

- \frac{6}{5} + 1

- 6 (4 - x) \leq - 4 (x + 1)

What is n/(n+1)+1/((n+1)(n+2)) ?
The solution to n/(n+1)+1/((n+1)(n+2)) is (n+1)/(n+2)