This kind of addition of two fractions is almost working as the "usual" way of adding fractions.
But before I start to explain how it works, we should create an example.
In this case it would be 3/7 + 5/8 (= 59/56).

First you need to multiply the numerator of the __first__ fraction with the denominator of the __second__ fraction.
So in this example you need the 3 of the __first__ fraction and the 8 of the __second__ fraction.

After that you do the same with the remaining numbers: Multiply the denominator of the __first__ fraction with the numerator of the __second__ fraction.
Put both products into the numerator and add them together
⇒ (3⋅8 + 7⋅5)/x = (24+35)/x = 59/x.

The new denominator consists of the product of the two denominators which you've got already. So multiply 7 and 8.
Put this result into the denominator ⇒ 59/ (7⋅8) = 59/56.
As you can see we've got the same result as in the second paragraph. Cool, isn't it?

But if you take a closer look you'll find out that this is almost the same way as the "regular" adding of two fractions.
Let's have a closer look …

… We multiply both numerators with both numbers of the other fraction.

7⋅5 and 7⋅8

8⋅3 and 8⋅7

In our "normal" addition it leads to fractions of same denominators.

In my opinion the Vedic Mathematics is easier than the 'normal' way of adding fractions.
Let's assume two big fractions like 56/65 + 34/43. I think it will be more difficult to multiply 56 and 43 😉.

Click on the "+" to try it yourself. Enter new values if you like: