QUESTIONS:
2014; 2bi
SUBTRACTING Rational
EXPRESSIONS
a -c
b d
=
ad
bd
Subtracting rational expressions requires
rewriting the expression with a common
denominator through cross multilpication
Subtracting rational expressions requires the original
terms to be rewritten over a common denominator. The
denominator of the rewritten term is created by multiplying
the denominator of the first term by the denominator of the
second term (b.d). The numerator of the rewritten term is
created by cross multiplication of both the original terms
(a.d - b.c).
Once the rewritten term has been created the next step
is to expand the numerator through multiplication of
terms. The denominator is not expanded and stays in
b.d form
-
bc
bd
=
ad-bc
bd
for instance
x+4
(x-2)
8x-3
2x 2
Once expanded the numerator can then be simplified by subtracting the right sided term(s) from the
left sided term(s).
Simple questions will require you to just
subtract rational expressios while higher level
questions will require you to do this before using
more complex skills
Subtracting rational expressions is the opposite
process to adding rational expressions
practice Question
Subtract
x+4
(x-2)
8x-3
2x 2
Step One
Step Two
Rewrite term with a
common denominator and expand
numerator through multiplciation
Simplify numerator to get
final rational expression
Rewrite over
common
denminator
Expand
numerator
through
multiplication
x+4
(x-2)
8x-3
2x2
x+4.2x2 - x(x-2).8x-3
(x-2).2x2
x+4.2x2
= 2x3+8x
Rewrite
Identify
common
factors
x.8x + x.-3 -2.8x -2.-3
(x-2).8x-3
=8x2-3x -16x +6
Rewrite
=8x2-19x +6
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2x3+8x - (8x2-19x +6)
2x3+8x - 8x2+19x-6
2x3+8x -8x2+19x +6
8x +19x
=27x
2x 3- 8x 2+27x +6
And get
2x 3- 8x 2+27x +6
2x2(x-2)