QUESTIONS:
2014; 2bii
2013; 1c
2012; 2ai
Simplifying Rational
EXPRESSIONS
x + bx + cx + d = (x+b)(x+c)
x + bx
x(x+b)
2
2
Simplifying algebraic fractions
by cancelling common factors in
the numerator and denominator
Rational expressions can be simplified by factorising the
numerator and denominator and canceling any common
factors.
The numerator and denominator can be in the form of
quadratic expressions (x +bx+c) and can therefore be
factorised by following the general rules of factorisation.
To find two common factors for factorising you may need to
try out several combinations of factors as many combinations may multiply to to give acbd but only one will multiply to
give acbd and add to give ad+bc
for instance
x2+ 7x -18
x2+ 9x
When factorising make sure you take into account
the + and - signs infront of the factors as:
+ = +.+ (12 = 3.4)
- = +.- (-12 = 3.-4)
+ = -.- (12 = -3.-4)
Simple questions will require you to just
simplify rational expressions while higher level
questions will require you to do this before using
more complex skills
practice Question
Simplify
x2+ 7x -18
x2+ 9x
Step One
Step Two
Identify common factors that
multiply to give d (-18) and
add to give bx+cx (7x)
Factorise expressions within
brackets and simpify
Find d
Identify
common
factors
x2+ 7x -18
x2+ 9x
-9.2=-18
9.-2=-18
multiply to -18, add to 7
9+-2=7
9.-2=-18
2
Rewrite
x -2x+9x -18
x2+9x
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Factorise numerator
and denominator
x2-2x+9x -18
x2+9x
Pull out common
multiples on each side
x(x -2) + 9(x -2)
x(x +9)
Identify factors in brackets
in numerator
x(x -2) + 9(x -2)
Form brackets and cancel
common brackets
(x+9)(x-2)
x(x+9)
And get
(x-2)
x
(x+9)(x-2)
x(x+9)