What is the simplified form of the quantity x over 3 minus y over 4 all over the quantity x over 4 plus y over 3?

= (x/4 + y/3) / (x/3 - y/4) = [ (3x+4y) / 12]/[ (4x - 3y) / 12] = (3x+4y) / (4x-3y)

First we write the expression:

((x / 3) - (y / 4)) / ((x / 4) + (y / 3))

We multiply the numerator and the denominator of the expression by: (4) * (3).

We have then:

(((4) * (3)) * ((x / 3) - (y / 4))) / (((4) * (3)) * ((x / 4) + (y / 3)))

We now rewrite the expression:

(4x - 3y) / (3x + 4y)

The simplified expression is:

(4x - 3y) / (3x + 4y)