October 2nd, 2016, 02:47 PM  #11 
Newbie Joined: Sep 2016 From: USA Posts: 14 Thanks: 3 
Ahh I see. For a moment I actually forgot what v8archie meant by the sum of 1/x + 1/y. I overestimated the problem too and was thinking too advanced. That's a fair point.

October 2nd, 2016, 03:06 PM  #12 
Senior Member Joined: Aug 2016 From: morocco Posts: 273 Thanks: 32 
$\frac{5}{4}=\frac{x+y}{xy}=\frac{x}{xy}+\frac{y}{ xy}=\frac{1}{y}+\frac{1}{x}$

October 2nd, 2016, 03:41 PM  #13 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,276 Thanks: 2437 Math Focus: Mainly analysis and algebra 
That's wrong and backwards. Rather than trying to be clever, just do the sum! 
October 2nd, 2016, 03:51 PM  #14 
Newbie Joined: Oct 2016 From: United States Posts: 2 Thanks: 0  
October 2nd, 2016, 04:02 PM  #15 
Newbie Joined: Oct 2016 From: USA Posts: 8 Thanks: 0  The steps to solve are reversed, and the result is inverted. I think this is how you "do the sum": $\displaystyle \frac{1}{x}+\frac{1}{y} $ Find a common denominator and multiply each fraction by 1 $\displaystyle \frac{y}{y}\cdot\frac{1}{x}+\frac{x}{x}\cdot\frac{ 1}{y}$ $\displaystyle \frac{y}{xy}+\frac{x}{xy}$ Add together $\displaystyle \frac{x+y}{xy}$ Substitute $\displaystyle \frac{4}{5}$ 
October 2nd, 2016, 04:06 PM  #16 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,276 Thanks: 2437 Math Focus: Mainly analysis and algebra 
You have been learning how to add fractions? So add $\frac1x + \frac1y$. I don't know what method you've been taught for that, so I prefer not to say how in case I confuse you (edrudathec gives one approach above, another involves "crossmultiplying"). But your denominator will be the product of the denominators of the two summands: $x \times y$. When you have found the sum of the two fractions, you will be able to see how to use the values you've been given.
Last edited by v8archie; October 2nd, 2016 at 04:08 PM. 
October 2nd, 2016, 05:26 PM  #17 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,276 Thanks: 2437 Math Focus: Mainly analysis and algebra 
Perhaps I should mention that the general rule with any mathematics problem you face is that you should start by thinking "what do I know how to do" with the problem. The answer should never be "nothing". The key to mathematics is to try things to see if they help. Sometimes, experience tells you that one approach is more likely to work than another, but it doesn't really matter. Mathematics is not about seeing what the answer is and writing it down. Mathematics is about recognising patterns, but also about playing with things. Try something. If it doesn't work, try something else. In this case, you are given two equations which you, quite reasonably, may not know what to do with. You might try something with them, but you will be likely to quickly reach a point that you can go no further (or you might follow GeoLifeScienceGuy's route and get somewhere that way). But, if you've been studying how to add fractions, it's quite likely that you can get to the solution by adding the fractions you've been given. Even if you don't yet see how that will help, it doesn't hurt to try it and see what you are left with. 
October 2nd, 2016, 07:04 PM  #18 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 12,130 Thanks: 801  
October 2nd, 2016, 07:16 PM  #19 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,788 Thanks: 1037 Math Focus: Elementary mathematics and beyond  
October 2nd, 2016, 07:29 PM  #20 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 12,130 Thanks: 801 
Greg, I was trying to "lengthen" this useless thread 

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