How do you subtract #(7w-1)/(w^2-3w-40)-(w-7)/(w^2-25)#?

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Answer 1 · 2016-09-13T21:34:18

#(3(2w^2-7w-17))/((w-8)(w+5)(w-5)#

When adding algebraic or arithmetic fractions, find a common denominator.

#(7w-1)/(w^2-3w-40) - (w-7)/(w^2-25)#

Factorise the denominators first

#(7w-1)/((w-8)(w+5)) - (w-7)/((w+5)(w-5))#

#LCD =color(red)((w-8)(w+5)(w-5))#

=#((7w-1)(w-5)-(w-7)(w-8))/((w-8)(w+5)(w-5)#

=#(7w^2-35w-w+5-(w^2-8w-7w+56))/((w-8)(w+5)(w-5)#

=#((7w^2-35w-w+5-w^2+8w+7w-56))/((w-8)(w+5)(w-5)#

=#((6w^2-21w-51))/((w-8)(w+5)(w-5)#

=#(3(2w^2-7w-17))/((w-8)(w+5)(w-5)#