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

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

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factor (k+1)/(k+2)+1/((k+1)(k+2))

factor

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

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

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Since the denominators are equal, combine the fractions:

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

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

Expand

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

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

2 x < 3 x + 2 < x + 6

2 x + 4 \leq 5 x + 3

\frac{200}{q} + 3 \geq 9000

4 z + 5.2 > 34.6 - 3 z

5 x^{2} + 7 x - 6

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