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受欢迎的代数 >

化简 (a^2-5a+6)/(3a-15)(6a)/(a^2-a-30)(a^2-25)/(2a-4)

解答

化简

\frac{a ^{2} - 5 a + 6}{3 a - 15} \cdot \frac{6 a}{a ^{2} - a - 30} \cdot \frac{a ^{2} - 25}{2 a - 4}

解答

\frac{( a - 3 ) a}{a - 6}

求解步骤

\frac{a ^{2} - 5 a + 6}{3 a - 15} \cdot \frac{6 a}{a ^{2} - a - 30} \cdot \frac{a ^{2} - 25}{2 a - 4}

使用分式法则:

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

= \frac{( a ^{2} - 5 a + 6 ) \cdot 6 a ( a ^{2} - 25 )}{( 3 a - 15 ) ( a ^{2} - a - 30 ) ( 2 a - 4 )}

因式分解

3 a - 15 : 3 (a - 5)

= \frac{( a ^{2} - 5 a + 6 ) \cdot 6 a ( a ^{2} - 25 )}{3 ( a - 5 ) ( a ^{2} - a - 30 ) ( 2 a - 4 )}

因式分解数字:

6 = 3 \cdot 2

= \frac{( a ^{2} - 5 a + 6 ) \cdot 3 \cdot 2 a ( a ^{2} - 25 )}{3 ( a - 5 ) ( a ^{2} - a - 30 ) ( 2 a - 4 )}

约分:

3

= \frac{( a ^{2} - 5 a + 6 ) \cdot 2 a ( a ^{2} - 25 )}{( a - 5 ) ( a ^{2} - a - 30 ) ( 2 a - 4 )}

因式分解

a^{2} - 25 : (a + 5) (a - 5)

= \frac{( a ^{2} - 5 a + 6 ) \cdot 2 a ( a + 5 ) ( a - 5 )}{( a - 5 ) ( a ^{2} - a - 30 ) ( 2 a - 4 )}

约分:

a - 5

= \frac{( a ^{2} - 5 a + 6 ) \cdot 2 a ( a + 5 )}{( a ^{2} - a - 30 ) ( 2 a - 4 )}

因式分解

a^{2} - a - 30 : (a + 5) (a - 6)

= \frac{( a ^{2} - 5 a + 6 ) \cdot 2 a ( a + 5 )}{( a + 5 ) ( a - 6 ) ( 2 a - 4 )}

约分:

a + 5

= \frac{( a ^{2} - 5 a + 6 ) \cdot 2 a}{( a - 6 ) ( 2 a - 4 )}

因式分解

2 a - 4 : 2 (a - 2)

= \frac{( a ^{2} - 5 a + 6 ) \cdot 2 a}{( a - 6 ) \cdot 2 ( a - 2 )}

约分:

2

= \frac{( a ^{2} - 5 a + 6 ) a}{( a - 6 ) ( a - 2 )}

因式分解

a^{2} - 5 a + 6 : (a - 2) (a - 3)

= \frac{( a - 2 ) ( a - 3 ) a}{( a - 6 ) ( a - 2 )}

约分:

a - 2

= \frac{( a - 3 ) a}{a - 6}

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