(Y√X+X√Y)/(XY-Y^2)-(X+√(XY)+Y)/(X√X-Y√Y)=?
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(Y√X+X√Y)/(XY-Y^2)-(X+√(XY)+Y)/(X√X-Y√Y)
=(Y√X+X√Y)/[Y(X-Y)]-(X+√(XY)+Y)/[(√X-√Y)(X+√(XY)+Y)]
=(Y√X+X√Y)/[Y(X-Y)]-1/(√X-√Y)
=(Y√X+X√Y)/[Y(X-Y)]-(Y√X-Y√Y)/[Y(X-Y)]
=[(X-Y)√Y]/[Y(X-Y)]
=1/√Y
=(Y√X+X√Y)/[Y(X-Y)]-(X+√(XY)+Y)/[(√X-√Y)(X+√(XY)+Y)]
=(Y√X+X√Y)/[Y(X-Y)]-1/(√X-√Y)
=(Y√X+X√Y)/[Y(X-Y)]-(Y√X-Y√Y)/[Y(X-Y)]
=[(X-Y)√Y]/[Y(X-Y)]
=1/√Y
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