Question

(5x)/(x-1) - (4x)/(x+1) I need to simplify this, but I forget how to do it.

Answer 1

find common denominator

Answer 2

When we do common denominator, it's like finding the common multiple between the two different denominators, and sum them up, since we know that same denominators actually do sum up.
So, in a generalized case:
\[\frac{ a }{ b }-\frac{ x }{ y }\]
Now, I have to find a way to make those denominators equal, but how?
Since both of these are multiplied by 1, and we can transform that "1" into something that would allow us to make those denominators equal.
The answer for that is "y/y" and "b/b", it'll look like this:
\[(\frac{ y }{ y })(\frac{ a }{ b })-(\frac{ x }{ y })(\frac{ b }{ b } ) \]
Since we know how to multiply fractions, you know, numerator-numerator, denominator-denominator:
\[\frac{ ya }{ yb }-\frac{ xb }{ yb }\]
Look at that, I made the denominators equal, and I can close everything up with the same denominator and just operate the numerators.
\[\frac{ ya-xb }{ yb }\]
Therefore, by transitivity:
\[\frac{ a }{ b }-\frac{ x }{ y }=\frac{ ya-xb }{ yb }\]
I have proven the "common denominator", but I think Raffle will do the rest.

Answer 3

@razorxwire
How to get -9x ?