First post as you can see. I'm doing high school maths and really need to improve. I can do every exercise in the basic algebra chapter except for these 2. I have no idea why, they've just stumped me.
So any help would be much appreciated.
You have to use the method here that you add a sum with the value zero to the numerator and to the denominator. I'll put the two summands in question into boxes:
Now re-arrange numerator and denomintor:
Now factorize numerator and denominator:
Now factor again and cancel the common factor which is: (4q - 3r)
I'll leave the rest for you.
There may be two reasons for your difficulty:Factor: .
. .  There are two variables
. .  That "2" in front.
Just as we "split" the first term into two factors,
. . we can do the same with the last term.
It looks like this: .
Since factors into .and factors into ,
. . we have: .
Now insert the signs that make the "middle term" come out to .
I'll take baby-steps . . .Simplify: .
Factoring the denominators, we have: .
To add or subtract fractions, we must have a common denominator.
. . In this problem, it is:
Now we must "convert" each fraction so it has in the denominator.
Multiply the first fraction by .
Multiply the second fraction by .
The problem looks like this: .
. . and we have: .
The fractions have a common denominator, so we can combine them.
. . Combine the numerators and "keep" the common denominator.
So we have: .
Are we done? . . . Well, no. .The fraction can be reduced.
And cancel the