Evaluate the difference quotient for the given function.
f(x) = (x+5)/(x + 2)

(f(x) − f(1))/(x − 1)

Question

Evaluate the difference quotient for the given function. 
f(x) = (x+5)/(x + 2)
   
(f(x) − f(1))/(x − 1)

anonymous · Answer

ick!

anonymous · Answer

lets make life easy and compute 
$$f(1)=\frac{1+5}{1+2}=\frac{6}{3}=2$$ forst

anonymous · Answer

so you have 
$$\frac{f(x)-2}{x-1}$$ as a start

anonymous · Answer

i should just quit.  i keep putting x + 1 when it is x + 2
this time for real
$$f(x)-2=\frac{x+5}{x+2}-2=\frac{x+5-2(x+2)}{x+2}$$
$$=\frac{x+5-2x-4}{x+2}=\frac{1-x}{x+2}$$ there now it is right!

anonymous · Answer

now divide by 
$$x-1$$ and get 
$$\frac{1-x}{(x-1)(x+2)}=\frac{-1}{x+2}$$

anonymous · Answer

because  
$$\frac{1-x}{x-1}=-1$$

anonymous · Answer

sorry i  messed up twice with those stupid typos. it is right now

anonymous · Answer

thank you for the step-by-step analysis!