Question 822588
{{{x/y + y/x= a}}} and {{{x/y - y/x= b}}}
We're looking for the value of {{{a^2-b^2}}}<br>
Probably the easiest way to figure this out is to recognize that there is a factoring pattern with {{{a^2-b^2}}} in it:
{{{a^2-b^2 = (a+b)(a-b)}}}<br>
To find {{{a^2-b^2}}} we will figure out what (a+b)(a-b) works out to be. Substituting the given expressions for a and b into (a+b)(a-b) we get:
{{{((x/y + y/x)+(x/y - y/x))((x/y + y/x)-(x/y - y/x))}}}
Note the use of parentheses! It is critical to use them like this when substituting in complex expressions.<br>
Now we simplify. In the a+b factor the y/x's cancel and in the a-b factor the x/y's cancel:
{{{(2x/y)(2y/x)}}}
Now when we multiply the x's cancel and the y's cancel leaving us with:
2*2 or 4