How do you combine #m/(20+9m+m^2)-4/(12+7m+m^2)#?

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Answer 1 · 2016-08-18T21:05:45

#((m-5))/((5+m)(3+m))#

Factorise the denominators first.

#m/(20+9m+m^2)-4/(12+7m+m^2)#

=#m/((5+m)(4+m))-4/((3+m)(4+m))#

#"Find a common denominator"#

=#(m(3+m) - 4(5+m))/((5+m)(4+m)(3+m))#

=#(3m +m^2 -20-4m)/((5+m)(4+m)(3+m))#

=#(m^2 -m-20)/((5+m)(4+m)(3+m))#

=#((m-5)(m+4))/((5+m)(4+m)(3+m))#

#((m-5)cancel((m+4)))/((5+m)cancel((4+m))(3+m))#