SOLUTION: I'm stuck on this one. Do I plug something into something? Not sure what book this is from. Let f(x)= 2/x + 1/x-1. Find all a for which f(a)= f(a+1). Thanks!

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I'm stuck on this one. Do I plug something into something? Not sure what book this is from. Let f(x)= 2/x + 1/x-1. Find all a for which f(a)= f(a+1). Thanks!      Log On


   

Question 44817: I'm stuck on this one. Do I plug something into something? Not sure what book this is from.
Let f(x)= 2/x + 1/x-1. Find all a for which f(a)= f(a+1).
Thanks!
Answer by adamchapman(301) About Me  (Show Source):
You can put this solution on YOUR website!
f(a)=f(a+1) means that the function has the same value x=1 and when x=(a+1)
f%28x%29=2%2Fx%2B1%2F%28x-1%29
so:
2%2Fa%2B1%2F%28a-1%29=2%2F%28a%2B1%29%2B1%2Fa
Now rearrange to find a:
2%2B%28a%2B1%29%2F%28a-1%29=2%28a%2B1%29%2B%28a%2B1%29%2Fa
2%28a-1%29%2B%28a%2B1%29=2%28a%2B1%29%28a-1%29%2B%28a%2B1%29%28a-1%29%2Fa
2a%28a-1%29%2B%28a%2B1%29a=2a%28a%2B1%29%28a-1%29%2B%28a%2B1%29%28a-1%29
2a%5E2-a%2Ba%5E2%2Ba=2a%28a%5E2-1%29%2B%28a%5E2-1%29
3a%5E2=2a%5E3-2a%5E2%2B%28a%5E2-1%29
3a%5E2=2a%5E3-a%5E2-1
2a%5E3-4a%5E2-1=0
Use this link:
http://www.1728.com/cubic2.htm
to find the root(s) of this equation.
I hope this helps.
P.S. I am trying to start up my own homework help website. I would be extremely grateful if you would e-mail me some feedback on the help you received to adam.chapman@student.manchester.ac.uk
Adam