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

1 Answer
May 19, 2018

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

Explanation:

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