
Arturo O. answered 02/08/18
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Note that the denominator of the last term is a difference of squares.
y2 - x2 = (y - x)(y + x) = -(x - y)(x + y)
Make -(x - y)(x + y) the common denominator by multiplying and dividing the first term by -(x + y), and the second term by (x + y), add the 3 terms, and get a numerator of
-(x + y)2 + x(x + y) - y = -x2 - 2xy - y2 + x2 + xy - y = -xy - y2 - y = -y(x + y + 1)
Divide the simplified numerator by the common denominator and get
-y(x + y + 1) / [-(x - y)(x + y)] = y(x + y + 1) / [(x - y)(x + y)]
That is the same as the book answer.