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

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

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simplify k/(k+1)+1/((k+1)(k+2))

simplify

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

\frac{k + 1}{k + 2}

Solution steps

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

Least Common Multiplier of

k + 1, (k + 1) (k + 2) : (k + 1) (k + 2)

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

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

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

Cancel

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

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

\frac{5 x - 3}{x + 1} \leq 4

3 + 5 x > - 17

(2 - 5 i)^{2}

\frac{2}{3} x - \frac{1}{3} x = \frac{7}{9} x + 1

(- \frac{1}{2})^{2}

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