`c)((5a+b)/(5a^2 - ab)+(5a-b)/(5a^2 + ab)):(100a^2 + 4b^2)/(25a^3 +ab^2) (a \ne 0; a \ne +- b/5)`

`=(((5a+b)^2)/(a(5a-b)(5a+b)) + ((5a-b)^2)/(a(5a-b)(5a+b))) : (4(25a^2 + b^2))/(a(25a^2+b^2))`

`=(25a^2 + 10ab + b^2 + 25a^2 - 10ab + b^2)/(a(5a-b)(5a+b)) . a/4`

`=(50a^2 + 2b^2)/(a(5a-b)(5a+b)) . a/4`

`=(2(25a^2+b^2) . a)/(a(5a-b)(5a+b) . 4)`

`=(25a^2 + b^2)/((5a-b)(5a+b) . 2)`

`=(25a^2 + b^2)/((25a^2 - b^2) . 2)`

`=(25a^2 + b^2)/(50a^2 - 2b^2)`