1. X and Y help!

X is not equal to Y

(x/y)+x = (y/x)+y

What is the value of (1/x) + (1/y)

2. Originally Posted by Slipknotfanatic89
X is not equal to Y

(x/y)+x = (y/x)+y

What is the value of (1/x) + (1/y)
And $\displaystyle x,y\not = 0$
Thus,
$\displaystyle \frac{x}{y}+x=\frac{y}{x}+y$
Thus,
$\displaystyle \frac{x}{y}-\frac{y}{x}=y-x$
Thus,
$\displaystyle \frac{x^2-y^2}{xy}=y-x$
Thus,
$\displaystyle \frac{(x+y)(x-y)}{xy}=y-x$
Thus, since $\displaystyle y-x\not =0$
$\displaystyle \frac{x+y}{xy}=-1$
Thus, (express fraction as),
$\displaystyle \frac{1}{x}+\frac{1}{y}=-1$

3. Originally Posted by ThePerfectHacker
Thus, since $\displaystyle y-x\not =0$
$\displaystyle \frac{x+y}{xy}=-1$
Thus, (express fraction as),
$\displaystyle \frac{1}{x}+\frac{1}{y}=-1$
I don't quite understand where you got -1 from. Also, how did you simplify the fraction in the last step?

4. Originally Posted by c_323_h
I don't quite understand where you got -1 from. Also, how did you simplify the fraction in the last step?
Because I divided both sides by $\displaystyle x-y$
But, $\displaystyle \frac{y-x}{x-y}=-1$