Question 66958
<pre><font size = 5><b>{{{ (x^(-1) + y^(-1))/x^(-1) }}}

simplify write the answers with all exponents positive 

You didn't put any parentheses to show where numerator
and denominator begin and end, so I can't tell whether 
you mean

{{{ (x^(-1) + y^(-1))/x^(-1) }}}

or whether you mean

{{{x^(-1) + y^(-1)/x^(-1)}}}
 
-----------------------------------

If it's the first way

{{{ (x^(-1) + y^(-1))/x^(-1) }}}

Use the rule: {{{A^(-n)}}}={{{1/A^(n)}}} to rewrite
all the terms in numerator and denominator

{{{ (1/x^(1) + 1/y^(1))/(1/x^(1))}}}

Now we can erase all the 1 exponents:

{{{ (1/x + 1/y)/(1/x)}}}

Now look at all the denominators in the main
numerator and the main denominator.  They are
x, y and y.  The LCD is then xy, so we multiply
by {{{(xy)/(xy)}}} but write it as{{{((xy)/1)/((xy)/1))}}}

{{{((xy)/1)/((xy)/1))}}}·{{{ ((1/x + 1/y))/(1/x)}}}

Now distribute the {{{(xy)/1)}}} in the numerator
and indicate the multiplication of the denominators

{{{(((xy)/1)(1/x) + ((xy)/1)(1/y))/(((xy)/1)(1/x))))/(1/x)}}}

Cancel the x's in the first term on top, and just get y
Cancel the y's in the second term on top, and just get x
and cancel the x's in the term on the bottom, and just get y

So the answer is just

{{{(y + x)/y}}}

Edwin</pre>