How do you multiply and simplify #\frac { 6a - 18a ^ { 2} } { 4a ^ { 2} + 4a + 1} \cdot \frac { 6a ^ { 2} + 5a + 1} { 9a ^ { 2} - 1} #?

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Answer 1 · 2017-07-30T08:18:47

#=(-6a)/((2a+1))#

#\frac { 6a - 18a ^ { 2} } { 4a ^ { 2} + 4a + 1} \cdot \frac { 6a ^ { 2} + 5a + 1} { 9a ^ { 2} - 1} #

As a first step in simplifying, factorise each expression.

#=(6a(1-3a))/((2a+1)(2a+1))xx ((2a+1)(3a+1))/((3a+1)(3a-1))#

Now cancel like factors:

#=(6a(1-3a))/((2a+1)cancel((2a+1)))xx (cancel((2a+1))cancel((3a+1)))/((cancel(3a+1))(3a-1))#

#=(-6a(-1+3a))/((2a+1)(3a-1))" "(larr"take out"-1" as a factor")/ #

#=(-6acancel((3a-1)))/((2a+1)cancel((3a-1))#

#=(-6a)/((2a+1))#