How do you simplify?

(a/2+b/3)/(a/2-b/3)

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`(a/2+b/3)/(a/2-b/3)`

Consider numerator `a/2+b/3`

LCM of 2 and 3 = 6 ,

multiply and divide Numerator by 6

`(6xx(a/2+b/3))/6=((6xxa)/2+(6xxb)/3)/6`

`=(3a+2b)/6`

similarly multiply and divide denominator by 6 and simplify

`(6xx(a/2-b/3))/6=((6xxa)/2-(6xxb)/3)/6`

`=(3a-2b)/6`

`(a/2+b/3)/(a/2-b/3)=((3a+2b)/6)/((3a-2b)/6)`

`=((3a+2b)/6)xx(6/(3a-2b))`

`=(3a+2b)/(3a-2b)`

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