Evaluate the difference quotient for the given function. Simplify your answer. f(x) = x + 7 /x + 2 , f(x) − f(3) /x − 3

Answer 1

f(x)=x+7/x+3

f(3)=10/5=2

difference quotient=f(x)-f(3)/x-3 =[{(x+7)/(x+2)}-2]/(x-3)=[(x+7-2x-4)/(x+2)]/(x-3) = [(-x+3)/(x+2)]/(x-3)

= -1/(x+2)

it is negative because numerator is -x+3=-(x-3) so it cancels with denominator with negative sign.