How do you divide and simplify #\frac { 6m ^ { 2} - m - 2} { 9m ^ { 2} - 4} \div \frac { 6m ^ { 2} - 4m } { 2m ^ { 2} + 3m }#?

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Answer 1 · 2018-06-02T15:39:12

#((2 m + 1)(2m+3))/(2(3m+1)(3m-1))#

You can invert either term and then multiply:

#\frac { 6m ^ { 2} - m - 2} { 9m ^ { 2} - 4} \div \frac { 6m ^ { 2} - 4m } { 2m ^ { 2} + 3m }#

is the same thing as:

#(6m^2-m-2)/(9m^2-4)*(2m^2+3m)/(6m^2-4m)#

now factor all the terms:

#((2 m + 1) (3 m - 2))/((3m+1)(3m-1))*(m(2m+3))/(2m(3m-2))#

Now cancel like factors:

#((2 m + 1)cancel((3 m - 2)))/((3m+1)(3m-1))*(cancel(m)(2m+3))/(2cancel(m)(cancel(3m-2)))#

#((2 m + 1)(2m+3))/(2(3m+1)(3m-1))#