How do you divide #\frac { a - 3} { 9a } \div \frac { a ^ { 2} - 12a + 27} { 10a ^ { 2} }#?

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Answer 1 · 2017-04-19T09:20:30

#(10a)/(9(a-9))=(10a)/(9a-81)#

Let's first turn the division into multiplication:

#(a-3)/(9a) -: (a^2-12a+27)/(10a^2)#

#(a-3)/(9a) xx (10a^2)/(a^2-12a+27)#

Let's now factor the right side denominator:

#cancel(a-3)/(9a) xx (10a^2)/((a-9)cancel((a-3)))#

#(10cancela^2)/(9cancela(a-9))#

#(10a)/(9(a-9))=(10a)/(9a-81)#