(3)/(4)(m+n)-(1)/(4)(m-n);m=(1)/(2),n=(1)/(3)

Question

`(3)/(4)(m+n)-(1)/(4)(m-n);m=(1)/(2),n=(1)/(3)`

Answer 1

`(3)/(4)(m+n)-(1)/(4)(m-n) = (14)/(24)`

Explanation:

Given

`(3)/(4)(m+n)-(1)/(4)(m-n);m=(1)/(2),n=(1)/(3)`

Required

Solve

To do this, we simply substitute values of m and n in the given expression

`(3)/(4)((1)/(2)+(1)/(3))-(1)/(4)((1)/(2)-(1)/(3))`

Evaluate the brackets

`(3)/(4)((3 + 2)/(6))-(1)/(4)((3-2)/(6))`

`(3)/(4)((5)/(6))-(1)/(4)((1)/(6))`

Open Brackets

`(15)/(24) - (1)/(24)`

Take LCM

`(15 - 1)/(24)`

`(14)/(24)`

Hence:

`(3)/(4)(m+n)-(1)/(4)(m-n) = (14)/(24)`