Calculus of a Single Variable, Chapter 2, 2.4, Section 2.4, Problem 70

You need to evaluate the equation of the tangent line at (9,1), using the formula:
f(x) - f(9) = f'(9)(x - 1)
Notice that f(9) = 1.
You need to evaluate f'(x), using the quotient rule, such that:
f'(x) =((x+4)'(2x-5) - (x+4)(2x-5)')/((2x-5)^2)
f'(x) = (2x-5 - 2x - 8)/((2x-5)^2)
f'(x) = -13/((2x-5)^2)
You need to evaluate the derivative at x = 9:
f'(9) = -13/((18-5)^2) =>< f'(9) = -1/13
Replacing the values into equation yields:
f(x) - 1= -(1/13)(x - 9)
Hence, evaluating the equation of the tangent line at the given curve, yields f(x) = 1 - (1/13)(x - 9).