document.write( "Question 822588: If x/y + y/x= a and x/y - y/x= b, then the value of (a square - b square) is equal to- \n" ); document.write( "

Algebra.Com's Answer #495012 by jsmallt9(3758) $\"\"$ $\"About$

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$\"x%2Fy+%2B+y%2Fx=+a\"$ and $\"x%2Fy+-+y%2Fx=+b\"$
\n" ); document.write( "We're looking for the value of $\"a%5E2-b%5E2\"$

\n" ); document.write( "Probably the easiest way to figure this out is to recognize that there is a factoring pattern with $\"a%5E2-b%5E2\"$ in it:
\n" ); document.write( " $\"a%5E2-b%5E2+=+%28a%2Bb%29%28a-b%29\"$

\n" ); document.write( "To find $\"a%5E2-b%5E2\"$ 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:
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\n" ); document.write( "Note the use of parentheses! It is critical to use them like this when substituting in complex expressions.

\n" ); document.write( "Now we simplify. In the a+b factor the y/x's cancel and in the a-b factor the x/y's cancel:
\n" ); document.write( " $\"%282x%2Fy%29%282y%2Fx%29\"$
\n" ); document.write( "Now when we multiply the x's cancel and the y's cancel leaving us with:
\n" ); document.write( "2*2 or 4
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