```C3 Algebraic Fractions Questions
June 2006
1.
(a) Simplify
3x 2  x  2
.
x2 1
(3)
3x 2  x  2
1
(b) Hence, or otherwise, express
–
as a single fraction in its simplest form.
2
x( x  1)
x 1
(3)
Jan 2008
1.
Given that
dx  e
2 x 4  3x 2  x  1
 (ax2 + bx + c) + 2
,
2
( x  1)
( x  1)
find the values of the constants a, b, c, d and e.
(4)
June 2009
7.
The function f is defined by
f(x) = 1 –
(a) Show that f (x) =
x 8
2
+
, x  ℝ, x ≠ −4, x ≠ 2.
( x  2)( x  4)
( x  4)
x3
.
x2
(5)
Jan 2007
f(x) = 1 –
2.
(a) Show that f(x) =
3
3
+
, x  –2.
x  2 ( x  2) 2
x2  x 1
, x  –2.
( x  2) 2
(4)
(b) Show that x2 + x + 1 > 0 for all values of x.
(3)
(c) Show that f(x) > 0 for all values of x, x  –2.
(1)
June 2007
2.
f(x) =
(a) Show that f (x) =
2x  3
9  2x
–
,
2
x2
2 x  3x  2
x>
1
2
.
4x  6
.
2x  1
(7)
(b) Hence, or otherwise, find f (x) in its simplest form.
(3)
Jan 2010
Jan 2011
June 2011
C3 Algebraic Fractions Questions ANSWERS (45 marks)
June 2006
Jan 2008
June 2009
Jan 2007
June 2007
Jan 2010
Jan 2011
June 2011
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