What is (a^2-5a+6)/(3a-15)*(6a)/(a^2-a-30)*(a^2-25)/(2a-4) ?

The solution to (a^2-5a+6)/(3a-15)*(6a)/(a^2-a-30)*(a^2-25)/(2a-4) is ((a-3)a)/(a-6)

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

simplify

\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}

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

Solution steps

\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}

Apply the fraction rule:

\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 )}

Factor

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 )}

Factor the number:

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 )}

Cancel the common factor:

3

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

Factor

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 )}

Cancel the common factor:

a - 5

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

Factor

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 )}

Cancel the common factor:

a + 5

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

Factor

2 a - 4 : 2 (a - 2)

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

Cancel the common factor:

2

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

Factor

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

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

Cancel the common factor:

a - 2

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

\frac{6}{22}

\frac{6}{52}

(mn + 8 a)^{2}

\frac{x ^{2} - 8 x + 16}{x - 4}

7 \cdot (- 3)

What is (a^2-5a+6)/(3a-15)*(6a)/(a^2-a-30)*(a^2-25)/(2a-4) ?
The solution to (a^2-5a+6)/(3a-15)*(6a)/(a^2-a-30)*(a^2-25)/(2a-4) is ((a-3)a)/(a-6)