" Life is not a problem to be solved but a reality to be experienced! "
© Copyright 2013 - 2024 KUDO.TIPS - All rights reserved.
a)
(a+b-c)/ab + (a-b+c)/ac - (-a+b+c)/bc
= {c(a+b-c) + b(a-b+c) - a(-a+b+c)}/abc
= {ac+bc-c² + ab-b²+bc + a²-ab-ac}/abc
= {a²-b²-c²+2bc}/abc
b)
(a+b)/a - a/(a+b) - ab/(a-b)
= {(a+b)(a+b)(a-b) - a(a)(a-b) - ab(a)(a+b)}/(a)(a+b)(a-b)
= {(a²+2ab+b²)(a-b) - a²(a-b) -a²b(a+b)}/(a²+ab)(a-b)
= {a³-a²b+2a²b-2ab²+ab²-b³ - a³+a²b - a³b-a²b²}/a³-ab²
= {2a²b-ab²-b³-a³b-a²b²}/a³-ab²
= b(2a²-ab-b²-a³-a²b)/a(a²-b²)