Simplify this (2a-b)/(a^2+ab) - (2b-a)/(b^2+ab) + (a-b)/ab?

Question

http://www.wolframalpha.com/input/?i=%282a-b%29%2F%28a^2%2Bab%29+-+%282b-a%29%2F%28b^2%2Bab%29+%2B+%28a-b%29%2Fab

Answer 1

(2a-b)/(a^2+ab) - (2b-a)/(b^2+ab) + (a-b)/ab

= (2a-b)/a(a+b) - (2b-a)/b(b+a) + (a-b)/ab

= [b(2a - b) - a(2b - a)+ (a - b)(a + b)] /ab(a + b)

= [2ab - b^2 - 2ab + a^2+ a^2 - b^2] /ab(a + b)

= 2(a - b)(a + b)/ab(a + b)

= 2(a - b)/ab

Answer 2

okay :) i am answering ur question ..



so u have --



2a-b / (a^2+ ab) - (2b - a ) / (b^2 + ab) + (a - b) /ab

= (2a-b)(b^2 + ab) - (2b -a) ( a^2 + ab) / (a^ + ab)(b^2 +ab) + a-b /ab

on multiplying and simplifying u will get ..just multiply and cancel out the equal and opposite terms!



= a^b + a^3 - b^3 - ab^/ (a^+ab)(b^2 + ab) + a-b /ab



= a^2 ( a+b) - b^2 ( a +b ) / ( a^ +ab )(b^2 + ab) + a-b/ab



= (a^2- b^2 ) (a+b) / a(a+b) b (a+b) + a-b/ab



= (a-b)(a+b).(a+b) / ab(a+b)(a+b) + a-b/ab



as a^2 - b^2 = (a+b)(a-b)



cancel out the common terms ..

= a-b / ab + a-b/ab

= 2(a-b)/ab ANSSSSSS

yay !!!!!! u got that dude!

Answer 3

(2a - b)/(a^2 + ab) - (2b - a)/(b^2 + ab) + (a - b)/ab

= (2a - b)/a(a + b) - (2b - a)/b(b + a) + (a - b)/ab

= [(2a - b)b - (2b - a)a + (a - b)(a + b)]/[ab(a + b)]

= (2ab - b^2 - 2ab + a^2 + a^2 - b^2)/(ab(a + b))

= (2a^2 - 2b^2)/(ab(a + b))

= 2(a + b)(a - b)/(ab(a + b))

= 2(a - b)/ab