Example 3 :
2
y + 1
+
3
y − 1
=
2(y − 1)
(y + 1)(y − 1)
−
3(y + 1)
(y − 1)(y + 1)
=
2y − 2
(y + 1)(y − 1)
−
3y + 3
(y − 1)(y + 1)
=
2y − 2 − 3y − 3
(y + 1)(y − 1)
=
−y − 5
(y + 1)(y − 1)
=
−(y + 5)
(y + 1)(y − 1)
Sometimes it is difficult to find a simple expression that is a multiple of two algebraic expres-
sions. When this is the case it is perfectly acceptable to multiply the two expressions together
even though this will not necessarily form the smallest common multiple. You should check
at the end of the calculation in the final fraction that there are no common factors in the
numerator and denominator; if there are, you can always cancel them to give an equivalent
but simpler fraction.
Exercises:
1. Simplify the following algebraic expressions:
(a)
x
3
+
x
2
(b)
m
7
−
m
5
(c)
4t
5
+
t
2
(d)
m+1
3
−
m−2
4
(e)
3m+4
7
+
m−1
2
(f)
y
y+1
−
y
y+3
(g)
5
t+1
+
4
t−3
(h)
3m
m+4
+
4m
m+5
(i)
4
y+1
−
5
y+2
(j)
7
4x
+
2
5xy
Section 2 Multiplication and Division
As in numerical fractions, the trick with simplifying the multiplication and division of algebraic
fractions is to look for common factors both before and after calculation. Once common factors
are cancelled out you get an equivalent fraction in its simplest form. Remember that dividing
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