If #f(x)=x/(x+6)#, find #f(a)#, #f(a+h)# and #(f(a+h)-f(a))/h#?

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Answer 1 · 2017-10-17T08:46:18

#f(a)=a/(a+6)#; #f(a+h)=(a+h)/(a+h+6)#

and #(f(a+h)-f(a))/h=6/((a+6)(a+h+6))#

As #f(x)=x/(x+6)#

#f(a)=a/(a+6)#

#f(a+h)=(a+h)/(a+h+6)#

and #(f(a+h)-f(a))/h=((a+h)/(a+h+6)-a/(a+6))/h#

= #(((a+h)(a+6)-a(a+h+6))/((a+6)(a+h+6)))/h#

= #(a^2+ah+6a+6h-a^2-ah-6a)/(h(a+6)(a+h+6))#

= #(6h)/(h(a+6)(a+h+6))#

= #6/((a+6)(a+h+6))#