因数 ((2a-2))/((2a^2-50))*((a^2-4a-5))/((3a+3))

解

因数

\frac{( 2 a - 2 )}{( 2 a ^{2} - 50 )} \cdot \frac{( a ^{2} - 4 a - 5 )}{( 3 a + 3 )}

\frac{a - 1}{3 ( a + 5 )}

解答ステップ

\frac{2 a - 2}{2 a ^{2} - 50} \cdot \frac{a ^{2} - 4 a - 5}{3 a + 3}

\frac{2 a - 2}{2 a ^{2} - 50} = \frac{a - 1}{( a + 5 ) ( a - 5 )}

= \frac{a ^{2} - 4 a - 5}{3 a + 3} \cdot \frac{a - 1}{( a + 5 ) ( a - 5 )}

\frac{a ^{2} - 4 a - 5}{3 a + 3} = \frac{a - 5}{3}

= \frac{a - 1}{( a + 5 ) ( a - 5 )} \cdot \frac{a - 5}{3}

分数を乗じる:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{( a - 1 ) ( a - 5 )}{( a + 5 ) ( a - 5 ) \cdot 3}

共通因数を約分する:

a - 5

= \frac{a - 1}{( a + 5 ) \cdot 3}