How do you simplify #(7x+14)/(7x^2-7x-42)#?

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Answer 1 · 2018-03-27T07:31:11

#color(blue)(1/(x-3))#

#(7x+14)/(7x^2-7x-42)#

Factor out 7 from numerator and denominator:

#(7(x+2))/(7(x^2-x-6))#

Cancel:

#(cancel(7)(x+2))/(cancel(7)(x^2-x-6))=((x+2))/((x^2-x-6))#

Factor denominator:

#((x+2))/((x+2)(x-3))#

Cancel:

#(cancel((x+2)))/(cancel((x+2))(x-3))=color(blue)(1/(x-3))#

This result could also be achieved by factoring the denominator at the beginning, but this is a bit more difficult than factoring in stages: