Algebraic Manipulations Worksheet With Answer Key Page 2
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1
2
3
4
5
6
71 − 56
33. Express as a single fraction in its simplest form
23. Factorise the following completely.
+
2
a
1
2
+
−
2
−
(a)
12
b
10
b
12
+
−
2
a
1
a
1
−
−
+
2
2
(b)
b
2
a
9
bc
18
ac
24. Factorise completely
−
2
+
2
+
+
34. Simplify
(27 3 ) (
x
x
6
x
9)
−
2
2
(a)
16
x
4
y
−
−
+
(b) 3
ac
7
c
18
ab
42
b
−
−
5
÷
2
1
35. Simplify
9 x
x
3
−
−
3
x
2
3
x
1
36. Factorise completely
−
25. Express as a single fraction
.
2
−
+
2
−
x
3
x
2
x
2
x
2 2
−
2
−
2
+
x y
9
x
9
y
81
−
2
5
x
4
k
=
37. Express as a single fraction in its simplest form
26. Given that
y
3
, express x in terms of k
+
6
x
(
)
+
3 2
y
1
1
1
−
+
and y .
(
)(
)
−
+
+
−
y
2
y
1
y
1
y
2
2
x
1
−
27. Express
as a single fraction in its
(
)
+
( )
−
2
x
2
3
x
4
( )
−
5
× −
2
a
a
−
(
)
2
0
3
−
÷
×
3 6
1
38. Simplify
a b
5
a b
4
simplest form.
2
2
b
r
=
− , express t in terms of p , q
−
−
28. Given that
p
q
2
2
39. Factorise
25
a
36(
b a
)
completely
t
and r .
3
1
−
40. Simplify
−
−
−
−
2
2
8
x
2
x
3 6
x
5
x
4
2
+
−
− .
29. Factorise completely
8
xy
12
y
6
xy
9
41. Express as a single fraction in its simplest form
3
2
−
+
−
30. (a) Express
as a single fraction in its
p
1
p
5
−
−
+
x
1 5
x
3
(
)
+
−
2
4 3
p
1
1 9
p
simplest form.
− −
−
2
b
b
4
ac
=
(b) Given that
x
, express c in
(
) (
)
−
+
+
+
2
2
2
a
27 3
x
x
6
x
9
42. Simplify
terms of a , b and x .
−
+
2
2
a
5
a
3
(c) Simply the expression
.
−
2
+
−
2
3
y
2
x
2
a
5
a
12
=
43. Given that,
x
express y in terms of x
4
y
31. Factorise completely
+
+
−
−
−
+
2
x
2
x
3
(3
x
2)
2(3
x
2) 1
−
44. Simplify
into a single expression
+
+
5
x
5 5
x
10
2
−
−
2
m
m
1
32. Simplify
− − +
m n
1
mn
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