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

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

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expand (k(k+2)+1)/((k+1)(k+2))

expand

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

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

Solution steps

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

Expand

(k + 1) (k + 2) : k^{2} + 3 k + 2

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

Expand

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

= \frac{k ^{2} + 2 k + 1}{k ^{2} + 3 k + 2}

Factor

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

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

Factor

k^{2} + 3 k + 2 : (k + 1) (k + 2)

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

Cancel the common factor:

k + 1

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

\frac{( p - q ) ^{3}}{5}

(e^{x + y} - e^{x}) d x + (e^{x + y} + e^{y}) d y

\frac{( h + 9 ) ^{2}}{h}

\frac{( 2 m + p ) n ^{2}}{( 2 k ^{2} \cdot m + p ) 2 k ^{3}}

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

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