How do you simplify #(9m²-16n²) /( 6m-8n)#?

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Answer 1 · 2018-05-19T05:23:00

#(9m^2-16n^2)/(6m-8n)# = #(3m+4n)/2#

First factorize #9m^2 - 16n^2#

#9m^2 - 16n^2# = #(3m-4n)(3m+4n)#

Check:
#(3m-4n)(3m+4n)# = #9m^2 + 12mn-12mn-16n^2#
#(3m-4n)(3m+4n)# = #9m^2 + cancel(12mn-12mn)-16n^2#
#(3m-4n)(3m+4n)# = #9m^2 -16n^2#

#(9m^2-16n^2)/(6m-8n)# = #((3m-4n)(3m+4n))/(6m-8n)#

#(9m^2-16n^2)/(6m-8n)# = #((3m-4n)(3m+4n))/(2(3m-4n))#

#(9m^2-16n^2)/(6m-8n)# = #(cancel((3m-4n))(3m+4n))/(2(cancel(3m-4n))#

#(9m^2-16n^2)/(6m-8n)# = #(3m+4n)/2#