Q1. Find the H.C.F of 9x2 - 4 y2 and 6x2 + 4xy
Q2. Find the L.C.M of 2x2 - 17x + 21 and x2 - 49
Q3. Find the L.C.M of 15(4x3 – 4x2 + x) and 35(2x2 – 7x + 3)
x 2 x 12
x 2 4x 21
Q4. Reduce to Simplest form:
2
Q5. Simplify: 2m n2
16 m
3m 12
27mn 4
3ab
9a 2 b 2
Q6. Reduce to lowest terms:
Q7. Simplify:
5a
6a 2b
8b
9a 3b
Q8. Simplify:
x y
x 2 xy
x 2 xy
x y
Q9. Simplify: 4y 2z
Q10. Simplify:
2x
18ab
4a
2x 2 x y z
1
2
a2
b
1
x 3 2x
2
x 1
Q11. Find the value of;
a 2 b2 c2
, ,
to the lowest common deno min ator.
Q12. Reduce the given fractions
bc ca ab
Q13. Find the H.C.F of x3 + 7x2 + 12x and x3 - 2x2 – 15x
Q14. Simplify: 2u – [2v – {w – 2(u + v – w)}]
Q15. Subtract
Q16. Add:
2x 3
5x 4
from
3x 1
3x 1
2x 1
x 1
and
5x 3
x 3
Q17. Find the L.C.M of x2 – 7x + 10 and x2 + x – 6
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Q18. Simplify:
a2
a
a 1 a2 1
Q19. Simplify the following rational expression:
x
x
1
5
1
5
x
x
1
5
1
5
Q20. Find the L.C.M 0f 12(x4 – x3 and 8(x4-3x3 + 2x2)
ANSWERS:
A1. H.C.F = (3x + 2y)
A2. L.C.M = (x –7)(x +7)(2x – 3)
A3. . 105 x (2x -1)2 (x – 3) (x-1)
A4.
x 4
x 7
A5.
2m
9 4 m n3
A6.
2a
27b 3
A7.
15a 16b
6 3a b
A8.
1
x2
A9. 2y + 4z
A10.
2
x 1 2x 3 2x 1
A11.
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A12.
a 3 b 3 c3
,
,
abc abc abc
A13. x (x +3)
A14. 3w – 4v
A15. 1
7x 2 7x 6
5x 3 x 3
A16.
A17. (x – 5)(x -2)(x + 3)
A18.
A19.
a
a
2
1
2 25x 2 1
25x 2 1
A20. 24 x3 (x – 1)(x – 2)
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