확장 (k(4k+5)+1)/((4k+1)(4k+5))

해법

확장

\frac{k ( 4 k + 5 ) + 1}{( 4 k + 1 ) ( 4 k + 5 )}

\frac{k + 1}{4 k + 5}

솔루션 단계

\frac{k ( 4 k + 5 ) + 1}{( 4 k + 1 ) ( 4 k + 5 )}

(4 k + 1) (4 k + 5)

확대한다:

16 k^{2} + 24 k + 5

= \frac{k ( 4 k + 5 ) + 1}{16 k ^{2} + 24 k + 5}

k (4 k + 5) + 1

확대한다:

4 k^{2} + 5 k + 1

= \frac{4 k ^{2} + 5 k + 1}{16 k ^{2} + 24 k + 5}

4 k^{2} + 5 k + 1

요인:

(4 k + 1) (k + 1)

= \frac{( 4 k + 1 ) ( k + 1 )}{16 k ^{2} + 24 k + 5}

16 k^{2} + 24 k + 5

요인:

(4 k + 1) (4 k + 5)

= \frac{( 4 k + 1 ) ( k + 1 )}{( 4 k + 1 ) ( 4 k + 5 )}

공통 요인 취소:

4 k + 1

= \frac{k + 1}{4 k + 5}