Evaluate the difference quotient for the given function2?

Question

f(x)=(x+3)/(x+1), (f(x)-f(1))/(x-1)

thanks for the help :)

Answer 1

f(1) = 2

thus

[f(x) - f(1)]/[x-1] = [((x+3)/(x+1)) - 2] / (x-1)

= [(x+3) - 2(x+1)] / (x^2 - 1)

= (-x +1) / (x^2 - 1)

= -1/(x+1) .. . . provided that x ≠ 1.