Please simplify step by step:

5/4a - 2/3b

Step-by-step 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)