SOLUTION: If x/y + y/x= a and x/y - y/x= b, then the value of (a square

SOLUTION: If x/y + y/x= a and x/y - y/x= b, then the value of (a square - b square) is equal to-

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-
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
and
We're looking for the value of

Probably the easiest way to figure this out is to recognize that there is a factoring pattern with in it:

To find 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:

Note the use of parentheses! It is critical to use them like this when substituting in complex expressions.

Now we simplify. In the a+b factor the y/x's cancel and in the a-b factor the x/y's cancel:

Now when we multiply the x's cancel and the y's cancel leaving us with:
2*2 or 4

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