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Answer:
We have studied procedures for working with fractions in earlier grades.
a
b
×
c
d
=
ac
bd
(b≠0;d≠0)
a
b
+
c
b
=
a+c
b
(b≠0)
a
b
÷
c
d
=
a
b
×
d
c
=
ad
bc
(b≠0;c≠0;d≠0)
Note: dividing by a fraction is the same as multiplying by the reciprocal of the fraction.
In some cases of simplifying an algebraic expression, the expression will be a fraction. For example,
x2+3x
x+3
has a quadratic binomial in the numerator and a linear binomial in the denominator. We have to apply the different factorisation methods in order to factorise the numerator and the denominator before we can simplify the expression.
x2+3x
x+3
=
x(x+3)
x+3
=x(x≠−3)
If x=−3 then the denominator, x+3=0 and the fraction is undefined.
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