Explanation:
I guess the simplification is aiming to bring both terms into one fraction with the same denominator (bottom part).
and I assume this expressing is actually
(5/4)×a - (2/3)×b
or
simply
5a/4 - 2b/3
if that is so, then :
the common denominator is the smallest (or lowest) common multiple of 4 and 3.
and that is here simply 12 (there is no smaller number that can both be divided by 4 and by 3 without remainder).
so, we need to bring both fractions to .../12 and then combine them.
how do I do that ?
I multiply each fraction with another fraction that has the overall value 1 (to and bottom numbers are equal) but changes the denominator to 12.
that way I don't change the value of the original fraction, but I only change is appearance.
so, what do I need to multiply 4 with to get 12 ?
right, 3.
that gives us
5a/4 × 3/3 = 3×5a/(4×3) = 15a/12
and what do I need to multiply 3 with to get 12 ?
right, 4.
2b/3 × 4/4 = 4×2b/(3×4) = 8b/12
alright !
now we write the original expression using its new looks :
15a/12 - 8b/12
and that is
(15a - 8b)/12
alternative :
what if the typing was actually correct, and we are dealing with
5/(4a) - 2/(3b)
we still need to bring both fractions to the same denominator.
we know the smallest common multiple of 4 and 3 is 12.
and the smallest common multiple of a and b is ... ab.
so, we need to bring everything the fractions of the form .../(12ab)
again, the same trick, we multiply with fractions of value 1 (to and bottom are equal) but that cover the denominator to the desired common denominator.
what do I need to multiply 4a with to get 12ab ?
well, 3b
so, we get
5/(4a) × 3b/(3b) = 5×3b / (4×3ab) = 15b/(12ab)
and what do we need to multiply 3b with to get 12ab ?
well, 4a.
2/(3b) × 4a/(4a) = 2×4a / (3×4ba) = 8a/12ba = 8a/(12ab)
and together this gives us
(15b - 8a)/(12ab)