What A is equal to as A is a constant?

Question

#f(x)= 5/x#
Then the expression #(f(x+h)−f(x))/h# can be written in the form
#A/(x(x+h))#,

I thought it would be #(f(x+h)−f(x))/h#, but its not. any ideas?

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Answer 1 · 2018-03-22T08:48:13

#A=-5#

#f(x)=1/x#

#(f(x+h)-f(x))/h=(5/(x+h)-5/x)/h=((5x)/(x(x+h))-(5(x+h))/(x(x+h)))/h=-(5h)/(xh(x+h))=-5/(x(x+h))#

#A=-5#