If F(x)=x^2+5x how do I find in simplest form F(p)-F(q)/p-q ?

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Answer 1 · 2018-05-22T01:08:42

#p + q + 5#

#f(x)=x^2+5x#

find:

#(f(p)-f(q))/(p-q)#

#(p^2+5p-(q^2+5q))/(p-q)# insert the function

#(p^2+5p-q^2-5q)/(p-q)# multiply through #-1#

#(p^2-q^2 +5p-5q)/(p-q)# rearrange

#((p+q)(p-q)+5(p-q))/(p-q)# difference of squares.

#((p-q)(p+q+5))/(p-q)# factor out #p-q#

#p + q + 5# cancel factors