簡約 (16-c^2)/(c^2+c-20)

解

簡約

\frac{16 - c ^{2}}{c ^{2} + c - 20}

- \frac{4 + c}{c + 5}

解答ステップ

\frac{16 - c ^{2}}{c ^{2} + c - 20}

因数

16 - c^{2} : (4 + c) (4 - c)

= \frac{( 4 + c ) ( 4 - c )}{c ^{2} + c - 20}

因数

c^{2} + c - 20 : (c - 4) (c + 5)

= \frac{( 4 + c ) ( 4 - c )}{( c - 4 ) ( c + 5 )}

(4 + c) (4 - c) = - (4 + c) (c - 4)

= \frac{- ( 4 + c ) ( c - 4 )}{( c - 4 ) ( c + 5 )}

共通因数を約分する:

c - 4

= \frac{- ( 4 + c )}{c + 5}

分数の規則を適用する:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{4 + c}{c + 5}