Algebraic Fractions Worksheet
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1
2Solutions to Past Paper Questions – Algebraic Fractions
15) (a) 2 × 5 = 10, so find two numbers which multiply to 10 and add to 7:
2 and 5
So 2x
2
+ 7x + 5 = 2x
2
+ 2x + 5x + 5
= 2x(x + 1) + 5(x + 1)
= (2x + 5)(x + 1)
3
5 x
(b)
x1
2 x5 x1
3 2 x5 5 x
=
2 x5 x1
6 x155 x
=
2 x5 x1
11 x15
=
2 x5 x1
1
1
1
23−1
4
2
16)
−
=
=
=
3 x
2 x
6 x
6 x
6 x
3 x
3 x −1 2 x3
2 x3
17)
(a) (3x – 1)(3x – 1)
(b)
=
3 x−1 3 x −1
3 x−1
2
3
1
13) (b)
=
x
2 x
3
43
1
=
2x
3
7
1
=
2x
3
Cross-multiply
7×3=1×2x
21=2x
x=10.5
3
3x
17) (a) (x + 1)(x + 2)
(b)
x1
x1 x2
3 x23x
=
x1 x2
3x63x
=
x1 x2
6x6
=
x1 x2
6 x1
=
x1 x2
6
=
x2
18) 7
x−1
x2
1
4
=
x2
x−1
7 x−7x2
4
x2
x−1
=
2
8 x−5
4
x
=
x−2
2
0
4 x
−4 x−3
=
0
2 x1
2 x−3
=
1
3
x =−
or x =
2
2
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