Ok first you must realise the difference between "terms" and "factors". A term is something in algebra which is separated from other things by either + or -.
e.g. 3xy+2x
The two terms here are 3xy and 2x.
A factor is something which is part of a product.
e.g. 3xy + 2x
In the first term, the factors are 3, x and y. And in the second term, the factors are 2 and x.
When cancelling algebraic fractions, you can only do it if the thing that you want to cancel is a
factor of both the numerator and the denominator.
e.g.
xx(x+2)x is a factor of the
whole of the numerator and is also a factor of the denominator so you cancel it to get:
1x+2=x+2Next example:
2xy(3z)2xy+3There are two terms on the numerator, 2xy and 3. 2xy is
not a factor of the numerator. 2xy
is a factor of the denominator but it has to be a factor of both in order to cancel. So you would leave this fraction as it is.
Now try simplifying these fractions:
a)
2(x+2)3(x+5)(x+2)b)
2z3x+2zc)
(x+3)(x+2)3(x+3)+5d)
(x+2)(x+1)3(x+2)+2(x+2)For d), try factorising the numerator.