#### Algebraic fractions.

Simplify :
x 2 - 3x
2x 2 + 10x
1.
2.

x 2 - x - 6
x 2 - 25
6x 2 - 21x
x 2 + 5x + 6
3.
4.

2x 2 - 3x - 14
x 2 + x - 6
2x 2 + 5x - 12
x 2 - 2x - 24
5.
6.

2x 2 - 11x + 12
2x 2 + 8x
ax - bx + ay - by
x 2 - 2xy + y 2
x 2 - 2xy - 3y 2
x 2 + 2xy - 3y 2
7.
8.
----------------------  X   -------------------
---------------------   X   ---------------------
x 2 - y 2
a 2 - 2ab + b 2
x 2 - 9y 2
2x 2 - 3xy + y 2
ax - ay + bx - by
ax - ay - bx + by
ax + by + ay + by
9.
----------------------  X   -----------------------  X   ---------------------------
ax + ay - bx - by
a 2 - b 2
ax - ay - bx + by
a 2 + 8a + 15
ab - 3a - 2b + 6
ab - 3a - 5b - 15
10.
----------------------  X   -----------------------  X   ---------------------------
ab + 3a - 2b - 6
a 2 - 3a - 15
ab - 3a + 5b - 15
a 2 - a - 6
a 2 - 2a - 3
a 2 + 2a + 1
11.
-------------------   ÷   --------------------  X   -----------------------
a 2 + 3a + 2
a 2 + 5a + 6
a 2 + 4a + 4
p 2 - p - 2
p 2 - 3p + 2
p 2 - 4p + 4
12.
-------------------   X   --------------------   ÷   -----------------------
p 2 + 5p + 6
p 2 - 1
p 2 + 4p + 3
2x 2 - x - 1
2x 2 - 7x + 3
x 2 - x - 2
13.
-------------------   ÷   --------------------   ÷   -----------------------
2x 2 - 3x - 2
x 2 + x - 6
2x 2 - 5x - 3
6a 2 - 7ab - 3b 2
2a 2 + ab - 6b 2
9a 2 - 3ab - 2b2
14.
-------------------   ÷   --------------------   ÷   -----------------------
2a 2 - 3ab - 2b 2
3a 2 - 8ab + 4b 2
2a 2 - 3ab - 2b 2
2x 2 + xy - y 2
x 2 - y 2
3x 2 - xy - 2y2
15.
-------------------   ÷   --------------------   X   -----------------------
4x 2 + 4xy - 3y 2
2x 2 + 3xy - 2y 2
6x 2 - 5xy + y 2
3p 2 + 8pq + 4q 2
4p 2 - 5pq - 6q 2
4p 2 + 11pq + 6q2
16.
-------------------     X   -------------------------    ÷   -----------------------
2p 2 - 7pq + 6q 2
10p 2 - 11pq + 3q 2
4p 2 - 8pq + 3q 2
a - b
a + b
3p + 2q
p - 3q
17.
18.
------------    +   ------------
------------   +  ------------
2a - b
a - 2b
p + 3q
2p + q
a - b
a + b
3p + 2q
p - 3q
19.
20.
------------    -   ------------
------------   -  ------------
2a - b
a - 2b
p + 3q
2p + q
a + b
2b
2a - b
p + 2q
2p + q
3p - 2q
21.
22.
------------   +  ------------   −  ------------
------------   −  ------------   +  ------------
a - b
a + b
a 2 - b 2
p - 2q
p 2 - 4q 2
p + 2q
x + 3
x - 2
x - 3
23.
-------------------   +   --------------------     -----------------------
x 2 + 3x + 2
x 2 - 1
x 2 + x - 2
x + 4
x - 3
x + 1
24.
-------------------     --------------------     -----------------------
x 2 + x - 2
x 2 - 4
x 2 - 3x - 2
y - 1
y - 6
2y - 3
25.
-------------------     --------------------   +   -----------------------
y 2 + 5y + 6
y 2 + y - 6
y 2 - 4
2a + 1
a - 5
3a + 2
26.
-------------------     --------------------   +   -----------------------
6a 2 + 5a - 6
6a 2 - 13a + 6
4a 2 - 9
a - 3b
a + b
2a - 3b
27.
-------------------     --------------------   +   -----------------------
2a 2 - 3ab - 2b 2
a 2 - 3ab + 2b 2
2a 2 - ab - b 2