Question 135041
y over x - x over y divided by 2 over y -2 over x
:
{{{y/x - x/y}}}
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{{{2/y - 2/x}}}
:
Place them over a common denominator
{{{((y*y - x*x))/(xy)}}}
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{{{((2x - 2y))/(xy)}}}
:
{{{((y^2 - x^2))/(xy)}}}
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{{{((2x - 2y))/(xy)}}}
:
Invert the dividing fraction and multiply:
{{{((y^2 - x^2))/(xy)}}} * {{{(xy)/((2x-2y))}}}
Cancel the xy's and you have:
{{{((y^2 - x^2))/((2x-2y))}}}
or
{{{((y^2 - x^2))/(2(x-y))}}}
:
:
I failed to notice that y^2 - x^2 is the difference squares & can be factored to
{{{((y-x)(y+x))/(2(x-y))}}}
Cancel (y-x) leaving us with:
{{{(x+y)/2}}}
:
:
I can't believe that I keep screwing this up:
In order cancel y-x we have to change the sign in the denominator. Make it a -2
{{{((y-x)(y+x))/(-2(y-x))}}}
Cancel (y-x) leaving us with:
{{{(x+y)/(-2)}}} = {{{-((x+y))/2}}}
:
Sorry if I got you thoroughly confused. Do you have any questions?