simplifying complex fraction: (3/8y + 5/6x) / (5/12xy)

[Lila]

Please don't freak when you read this question. It's easier than it looks (I think!). I am just dumb and not sure how to answer it.
My textbook doesn't explain this method and I don't have a teacher so I'm stuck.
(3/8y + 5/6x) / (5/12xy)
The answer is:
(9x + 20y) / 10
I am not sure how to add two fractions that have completely different denominators. How did they do this?
Can anyone help me, please?
Thanks!

[stapel_eliz]

My textbook doesn't explain this method and I don't have a teacher so I'm stuck.
(3/8y + 5/6x) / (5/12xy)
The answer is:
(9x + 20y) / 10
I am not sure how to add two fractions that have completely different denominators. How did they do this?

To learn how to add rational expressions (that is, polynomial fractions), try this lesson. (If you need to review how to work with numerical fractions, try this review.)

To learn how to simplify "complex" fractions (which is the term for this sort of expression), try here.

[Lila]

Hi, that was helpful but not what I was looking for I'm afraid :(
How do I add two fractions that have different pronumerals in the denominator? So if I had:
3/a + 4/b
How would I simplify that?
Hope there is a way to do this, otherwise I'll have to call the publishers of the textbook and ask them!

[stapel_eliz]

How do I add two fractions that have different pronumerals in the denominator?

Fractions with variables in the denominators are called "rational expressions". The method for adding rational expressions (that is, polynomial fractions) is exactly the same as for adding numerical fractions.

Since the lessons on fractions and adding rational expressions do not relate to what you are attempting, you must mean something other than just adding things like 3/a and 4/b, something other than simplifying 3/a + 4/b. However, I'm afraid I can't figure out what this "something other" might be...?

[Lila]

okay, I don't know what's going on either!
How do I simplify 3/a + 4/b? Would the LCM be 1?

[stapel_eliz]

How do I simplify 3/a + 4/b? Would the LCM be 1?

Since 1 is not a multiple of and , no, this cannot be the Least Common Multiple.

To learn how to find LCMs of variable expressions, please try here. To see worked examples of this process, please review the lesson (provided earlier) on adding rational expressions.

[Lila]

oh okay, I'll check it out. Thanks so much!