1. Number
H)
m +1
2
−
m −1
3
m +1
5
=
3(m +1)
6
−
2(m −1)
6
×
5
m +1
=
3m +3− 2m + 2
6
×
5
m +1
=
(3m − 2m)+(3+ 2)
6
×
5
m +1
Answer =
5(m + 5)
6(m +1)
Number
I)
3
pq
×
4p
p+1
You cancel out the p from the pq and from the 4p
This leaves the 4 on the top without the p and the q on the
bottom without the p.
=
12
q(p+1)
You don't need to simplify any further

2. Number
J)
Simplify:
8(x +3)
9
×
12(x +1)
4(x +3)
=
8(x +3)
3
×
3(x +1)
(x +3)
Answer =
8(x +1)
3
In the above, we cancelled out the 2 (x +3) and the
two 3's to leave us with the answer given.
You don't expand the brackets out with the answer
as it is simplified already.