ALGRBRAIC FRACTIONS - PAST PAPER QUESTIONS
1.
Express as a single fraction in its simplest form:
2.
a)
Factorise:
b)
Hence simplify:
3
+
2
𝑝+5
4𝑥 2 − 𝑦 2
Simplify:
4.
a)
Factorise:
b)
Hence simplify:
4𝑥 2 − 𝑦2
6𝑥+3𝑦
𝑝2 − 4𝑞 2
1
𝑝2 − 4𝑞 2
3𝑝+6𝑞
(𝑥 + 4)2
Simplify:
6.
Simplify:
7.
Express
8.
Express as a single fraction
9.
Simplify:
10.
Express
11.
Express
12.
Express
13.
Express
14.
Simplify:
15.
Express
16.
Express
17.
Express
18.
Express
3
𝑥+2
𝑦3
×
𝑦2
2
𝑥3
5
+
𝑥 ≠ −2, 𝑥 ≠ 1 as a fraction in its simplest form.
𝑥−1
𝑎
𝑏
𝑏
+ 𝑎, 𝑎 ≠ 0, 𝑏 ≠ 0
3𝑥 − 15
𝑥
4
−
𝑠2
×
𝑡
3𝑡
4
+
𝑥− 1
2
as a fraction in its simplest form.
2𝑠
2
𝑎
𝑥 ≠ 0, 𝑥 ≠ −1 as a single fraction in its simplest form.
𝑥+1
𝑥 ≠ 1, 𝑥 ≠ −2 as a single fraction in its simplest form.
𝑥+2
3
−
(𝑎 + 4)
𝑎 ≠ 0, 𝑎 ≠ −4 as a single fraction in its simplest form.
(2𝑥 + 5)2
(2𝑥 − 1)(2𝑥 + 5)
5𝑝2
8
÷
𝑝
2
3
(𝑥 + 1)
𝑎
𝑏
×
−
3𝑏
4
(𝑥 + 3)
as a fraction in its simplest form.
1
(𝑥 − 2)
𝑥 ≠ −1, 𝑥 ≠ 2 as a single fraction in its simplest form.
as a fraction in its simplest form.
𝑎2
+
3
𝑥
3
2
2
(𝑥 − 5)2
3
2
3
𝑥 2 − 𝑥 − 20
𝑥6
2
3
(𝑚+1)
5.
2
1
4
+
3.
𝑚
1
𝑝
𝑥 ≠ −3, 𝑥 ≠ 0 as a single fraction in its simplest form.
3
2
3
3
1
3
3
2
3
2𝑥 + 2
19.
Simplify:
20.
Express
21.
Express
22.
a)i)
a)ii)
Factorise:
Factorise:
b)
Hence express
23.
Express
24.
Simplify:
25.
Express
2
(𝑥 + 1)2
𝑎
−
𝑥
1
+
𝑥2
7
𝑥+ 5
𝑏
𝑥 ≠ 0, 𝑦 ≠ 0 as a fraction in its simplest form.
𝑦
1
𝑥 ≠ 0 as a fraction in its simplest form.
𝑥
3𝑦 2 − 6𝑦
𝑦2 + 𝑦 − 6
3
−
𝑥
3𝑦 2 −6𝑦
𝑦2 + 𝑦 − 6
𝑥 ≠ −5, 𝑥 ≠ 0 as a single fraction in its simplest form.
𝑥 2 − 4𝑥
𝑥2
5𝑡
𝑠
÷
+ 𝑥 − 20
𝑡
2𝑠2
in its simplest form.
2
2
1
2
2
3
3
3