1 - a/(1 - a/(a + 1))
= 1 - a/((a + 1)/(a + 1) - a/(a + 1))
= 1 - a/((a + 1) / (1/(a + 1)))
= 1 - a/((a + 1) * (a + 1))
= 1 - a/(a + 1)2
= (a + 1)2/(a + 1)2 - a/(a + 1)2
= (a2 + 2a + 1)/(a + 1)2 - a/(a + 1)2
= (a2 + a + 1)/(a + 1)2
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(x + y)/2/(x2 - y2)
= (x + y)/(2*(x2 - y2))
= (x + y)/(2*(x + y)*(x - y))
= 1/(2*(x - y))