Name
Alg1
3/27/17
Rational Expressions Packet
1-Step Factoring: Factor each quadratic. If the quadratic is unable to be factored, your
answer should be PRIME.
Examples:
(last sign +)
x2 – 10x + 24
Same sign, both Factors of 24, sum of 10
(x – 6)(x – 4)
(last sign - )
x2 + x – 12
Different Signs
Factors of 12, diff. of 1
(x + 4)(x – 3)
1) x2 + 5x + 4
2) a2 – 12a + 35
3) f2 – 3f – 18
4) g2 + 5g – 50
5) t2 – 2t + 48
6) x2 – 100
7) s2 – 9s + 20
8) j2 + 7j + 12
9) k2 + 2k – 24
10) x2 – 6x – 7
11) n2 -25
12) c2 – 13c + 40
13) g2 – 5g – 84
14) z2 + 17z + 72
15) q2 – 3q + 18
16) p2 – 81
17) w2 – w – 132
18) x2 + 13x – 48
(D.O.T.S)
x2 – 49
Diff of Two Sq.
(x + 7)(x – 7)
1
Name
Alg1
3/27/17
Rational Expressions Packet
19) z2 + 9z – 36
20) h2 + 12h + 36
21) r2 + 5r – 36
22) b2 – 5b – 36
23) x2 – 36
24) m2 – 20m + 36
25) y2 – 4y – 60
26) v2 + 17v – 60
27) r2 + 7r – 60
28) x2 + 61x + 60
29) g2 – 23g + 60
30) b2 – 121
31) a2 + 4a – 96
32) y2 – y – 110
33) x2 + 33x + 90
34) t2 + 21t + 108
35) w2 – 64
36) x2 – 14x + 49
2
Name
Alg1
3/27/17
Rational Expressions Packet
Rational Expressions
Multiplication and Division
Factor each numerator and denominator.
Reduce where possible.
Keep what’s left.
1)
x3 + 4x2 – 77x . ●
32x2 – 50
32x - 40
x3 – 7x2
2)
3x2 – 48
x2 + 10x + 24
9x2 + 9x - 180
x2 + 11x + 30
.
÷
3
Name
Alg1
3/27/17
Rational Expressions Packet
Multiplication and Division:
DO ALL PROBLEMS WITH FACTORING DONE (STEP BY STEP) ON THE SIDE!
1)
6x3 - 48x2 .
x2 - x - 56
3)
10x3 - 360x .
4x2 + 24x
·
x2 + 18x +77.
3x2 - 363
· x2 + 7x + 6.
5x2 - 25x - 30
2) x2 + 15x + 54
x2 – 81
÷
x2 - 6x - 72 .
x2 - 21x + 108
4) x2 - 13x + 42 ÷
x2 – 4x - 21
x2 - 2x - 24 .
3x + 12
4
Name
Alg1
5) x2 + 4x - 96 .
x2 - 144
·
x2 - 4x - 96
x + 16x + 64
2
3/27/17
Rational Expressions Packet
6) x2 - 16x + 55 ÷
x2 - 25
4
3
6x – 66x
8x3 + 40x2
ANSWER KEY:
1)
2x2
(x - 11)
2) 1
3) x + 6
2
4) 3
(x+3)
5) x - 8
x+8
6) 4
3x
5
Name
Alg1
3/27/17
Rational Expressions Packet
Addition and Subtraction:
REMINDER: You need a COMMON DENOMINATOR to add and subtract fractions!
1)
5x + 88 . +
7x - 40
x+4
x+4
2)
4
x + 10x + 24
2
.
-
x
x + 3x -18
2
6
Name
Alg1
3/27/17
Rational Expressions Packet
Addition and Subtraction:
FIND THE COMMON DENOMINATOR 1st!!!!!!
1)
3)
x2 - 12x - 15 . +
x2 - x - 30
3x2 – 12x - 13 .
x2 - x - 30
5
. +
2x
.
2
6x - 42
x - 2x - 35
2)
10x - 9
3x + 12
4)
11
x - x - 20
2
-
-
7x - 18
3x + 12
.
4x
.
2
x - 16
7
Name
Alg1
5)
x+4
. + x-3 .
2
x - 2x - 48
4x2 - 32x
7)
6)
7x - 15 . + x - 9 .
x2 + 11x + 24
x+3
8)
3/27/17
Rational Expressions Packet
x+3
x-1
.
2
2
x - 49
x + 3x - 28
x+2
x2 - 196
-
x+5
.
x2 - x – 210
ANSWER KEY:
1) 4(x-7)(x+1)
(x-6)(x+5)
2) x + 3
x+4
3) 17x + 25 .
6(x-7)(x+5)
4) - 4x2 +31x - 44
(x-5)(x+4)(x-4)
5) 5x2 + 19x - 18 . 6) 7x - 19
4x(x-8)(x+6)
(x-7)(x+7)(x-4)
8
Name
Alg1
3/27/17
Rational Expressions Packet
Practice:
1)
3)
x2 + 2x - 35 .
x2 - 49
·
3x2 – 21x .
6x - 30
12x - 20 . ·
2x2 - 14x
x3 - 7x2 .
9x2 – 25
2)
x2 - 64
x + 14x + 48
÷
x2 -3x - 40
x2 + x - 30
·
x2 – 2x - 63
x2 – 3x – 54
2
4) x2 – x - 42
x2 - 49
.
.
9
Name
Alg1
5) x2 + 5x - 24 .
x2 + 19x + 88
7)
4x2 – 9
x2 - 9
. ÷
÷
3x2 – 9x .
6x2 - 726
16x2 - 24x .
4x - 12
3/27/17
Rational Expressions Packet
6) x2 - 4x - 12
÷
x2 - 36
.
2
2
x + 4x - 12
x + 8x + 12
8) x2 – 10x - 24
x2 - 144
·
x2 + 9x - 36.
x2 – x - 6
10
Name
Alg1
9) 2x2 + 4x - 48 .
6x + 36
11)
·
24x2 + 96x .
4x2 - 64
24x - 120 . · 49x2 - 9 .
14x - 6
6x2 - 150
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Rational Expressions Packet
10) x2 – x - 132
÷
x2 – 15x + 36 .
2
x + 6x - 55
x2 – 8x + 15
12) x2 – x - 90
x2 – 14x + 40
÷
x2 +15x + 54 .
6x – 24
11
Name
Alg1
13) x2 + 2x - 25 . + 3x2 – 2x .
2x - 5
2x - 5
15)
3x .
x+2
+
5
x-3
.
14)
16)
3/27/17
Rational Expressions Packet
13x - 9
7x - 31
.
3x + 11
3x + 11
4
x - 11
+
5x
.
x2 – 121
12
Name
Alg1
17) 11x
.
2
x – 3x - 18
19)
-
x - 8
. +
x + 13x + 42
2
3 .
x+3
x+3 .
x – x - 42
2
3/27/17
Rational Expressions Packet
18)
5
x
.
2
2
x – x - 20
x – 25
20)
x - 2 3x2 - 24x
x +9
.
2
x – x – 32
13
Name
Alg1
21) x - 1
. +
x + 11 .
2
2
x - 81
x – 10x + 9
22)
x2 + 2x - 25 .
x2 + 7x - 18
-
3x – 4 .
9x + 81
3/27/17
Rational Expressions Packet
22) 4x - 11 10 - 5x
.
3x - 7
3x – 7
24)
x-7
x + x - 12
2
+
x-2
.
x + 3x – 4
2
14
Name
Alg1
3/27/17
Rational Expressions Packet
Answer Key:
1) x _
2
2) x – 5 _
x+5
3)
2 _
3x + 5
7) 2x + 3
2x(x+3)
8) 1
9)
2x
13) 2x + 5
17) 8x + 18
(x-6)(x+3)
21) 2x2 + 18x +100
(x-9)(x+9)(x-1)
14) 2
4) 1
5) 2(x – 11) _
x
10) 1 11) 2(7x + 3) _
x+5
15) 9x2 – 4x +10 _
(x+2)(x-3)
6) (x+2)(x+2)
(x-2)(x+6)
12)
6 _
x+6
16) 49x + 44 _
(x+11)(x-11)
18) –x2 + x + 25
19) 2x2 – 5x – 77_ 20) -2x2-25x-8 _
(x+5)(x-5)(x+4)
(x+7)(x-7)(x+6)
3x(x-8)(x+4)
22) 3
23) 6x2 + 28x -233 _ 24) 2x2 – 17x + 13 _
9(x+9)(x-2)
(x+4)(x-3)(x-1)
15