Question

This is a basic math concept insight. Please don't confuse this with a question.
\[\text{Why are rational expressions cross-multiplied to get the answer?}\]

Answer 1

Do you remember addition of fractions? You do, so let's take an example.
\[\Large {5 \over 7} + {5 \over 8} \]
To get the denominators equal. You take the LCM. i.e. 56. So, you're basically multiplying 7 by 8 and you get 56.
Now, you multiply 7 by 8. You have to multiply 5 by 8 too. Now, observe that 5 is diagonal to 8. So you can say that it is cross multiplied.
\[\Large {6 \over x + 4}*{7 \over x + 1} \]
You can solve this using the same property. Any further questions are welcome.

Answer 2

Lol I meant + not *

Answer 3

Hmm \[\frac a b + \frac c d = \frac {ad+bc}{bd} \]

This is the *definition* of addition of two rational numbers.

The rules for addition, multiplication, and equality of our symbols are established by us and are not imposed upon us by any prior necessity other than that of coherency and usefulness for applications. So please don't confuse it with something else.

Answer 4

Exactly