Question

Match each expression with its simplified form.

1. a/(a^2-4)+2/(3a+6)
2.5/a+7
3.a/ab-3/b
4.6/ab+8/a
5.3a/4b^2-b/6a

Answer 1

`(a)/(a^2-4)+(2)/(3a+6) = (a)/((a-2)(a+2)) + (2)/(3(a+2)) = \\\\(3a)/(3(a-2)(a+2))+(2(a-2))/(3(a+2)(a-2)) = \\\\(3a+2a-4)/(3(a^2-4)) = (5a-4)/(3a^2-12)`


`(5)/(a)+7 = (5)/(a)+(7a)/(a) = (7a+5)/(a)\\\\\\(a)/(ab)-(3)/(b) = (1)/(b) -(3)/(b) = (1-3)/(b) = -(2)/(b)\\\\(6)/(ab)+(8)/(a) = (6)/(ab)+(8b)/(ab) = (6+8b)/(ab)\\\\(3a)/(4b^2) - (b)/(6a) = (9a^2)/(12ab^2) - (2b^3)/(12ab^2) = (9a^2-2b^3)/(12ab^2)`