October 2nd, 2016, 12:35 PM  #1 
Newbie Joined: Oct 2016 From: United States Posts: 2 Thanks: 0  Hard Fraction problem
I'm having quite a bit of trouble with this question. If x + y = 4 and xy = 5, then 1/x + 1/y = ? (Note: 1/x and 1/y are written were written in fraction form) 
October 2nd, 2016, 01:08 PM  #2 
Newbie Joined: Oct 2016 From: USA Posts: 7 Thanks: 0 
There are no real solutions. I'll try and figure out what the complex ones are. EDIT: This is false. It ends up with one real solution. I underestimated this problem. EDIT: No, wait, I overestimated it. Last edited by edrudathec; October 2nd, 2016 at 01:23 PM. 
October 2nd, 2016, 01:12 PM  #3 
Senior Member Joined: Sep 2015 From: CA Posts: 749 Thanks: 398  
October 2nd, 2016, 01:13 PM  #4 
Math Team Joined: Dec 2013 From: Colombia Posts: 6,390 Thanks: 2100 Math Focus: Mainly analysis and algebra  This is incorrect. Complex numbers are not required for this problem, only fractions. Have you tried doing the sum $\frac1x + \frac1y$? Last edited by v8archie; October 2nd, 2016 at 01:17 PM. 
October 2nd, 2016, 01:25 PM  #5 
Newbie Joined: Sep 2016 From: USA Posts: 14 Thanks: 3 
Try thinking of it like x + y = 4 xy = 5 xy  1 = 4 x + y = xy  1 And then divide and substitute xy to solve from there. 
October 2nd, 2016, 01:30 PM  #6 
Newbie Joined: Oct 2016 From: USA Posts: 7 Thanks: 0 
Trying to solve for x and y (which is what I did) is not a good way to solve this, because they're both complex numbers.

October 2nd, 2016, 01:31 PM  #7 
Math Team Joined: Dec 2013 From: Colombia Posts: 6,390 Thanks: 2100 Math Focus: Mainly analysis and algebra 
Given that it is described as a fractions problem, I am 95% certain that the OP is supposed to evaluate the sum he was given.

October 2nd, 2016, 01:44 PM  #8 
Newbie Joined: Sep 2016 From: USA Posts: 14 Thanks: 3 
I didn't mean solve it that way: solve for x=? and y=? Like if you divided and substituted xy then: x + y = xy  1 (Divide by xy) 1/y + 1/x = 1  1/xy (xy = 5) 1/x + 1/y = 1  1/5 Answer: 4/5. No complex numbers involved. I laid out the steps divide and substitute xy so that if u tried them you would see that the sum could easily be solved for. Last edited by GeoLifeScienceGuy; October 2nd, 2016 at 01:47 PM. 
October 2nd, 2016, 02:15 PM  #9  
Newbie Joined: Oct 2016 From: USA Posts: 7 Thanks: 0  Quote:
I wasn't sure what you meant by divide and substitute xy at first, so I advocated for v8archie's solution, which I think is the best out of the three. Sorry for the confusion.  
October 2nd, 2016, 02:16 PM  #10 
Math Team Joined: Dec 2013 From: Colombia Posts: 6,390 Thanks: 2100 Math Focus: Mainly analysis and algebra 
It is even easier, and better practice for the OP to simply do the given sum.


Tags 
fraction, hard, problem 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Fraction problem  Lilred  Elementary Math  3  February 1st, 2016 07:07 PM 
A fraction problem  shunya  Elementary Math  5  December 29th, 2015 10:43 AM 
Fraction inequality (hard)  matisolla  Algebra  5  June 4th, 2015 05:59 PM 
Hard fraction questions (Homework)  sharp  Elementary Math  9  September 25th, 2010 10:31 PM 
Fraction problem  clayson  Elementary Math  1  October 4th, 2009 06:15 AM 