Download 1. Perform the indicated operation and simplify your answer: a. x2

1. Perform the indicated operation and simplify your answer:
x2 − 6x + 9 x2 − 4x − 5
·
a. 2
x − 3x − 10 x2 − 2x − 3
x−3
Ans:
x+2
x2 + 2x − 15 x2 − 25
b. 2
·
x + x − 12
x+4
(x − 5)(x + 5)2
Ans:
(x + 4)2
2 − x x2 + 4x + 4
·
c. 2
x − 2x
x2 − 4
−(x + 2)
Ans:
x(x − 2)
x2 + 3x + 2 (x + 1)2
÷
d.
2x3
10x
5(x + 2)
Ans: 2
x (x + 1)
10 − 20x 2x2 + 7x − 4
÷ 2
e. 2
x − 2x
x + 2x − 8
10
Ans: −
x
2
4x + 10 6x2 + 15
÷ 2
f.
x−3
x −9
2(x + 3)
Ans:
3
2. Find the quotient and remainder by performing long division:
a. (x2 − 3x − 10) ÷ (x + 1)
6
Ans: (x − 4) −
x+1
5
4
b. (−2x + 3x − 2x2 + x − 1) ÷ (x2 − 1)
x
Ans: (−2x3 + 3x2 − 2x + 1) − 2
x −1
c. (3x6 + 1) ÷ (x2 − 2x + 2)
−24x + 25
Ans: (3x4 + 6x3 + 6x2 − 12) + 2
x − 2x + 2
d. (−x3 + 4x2 + 4x + 4) ÷ (x2 + x + 1)
1
Ans: (−x + 5) − 2
x +x+1
e. (−4x4 + 3x3 − x) ÷ (x − 3)
Ans: (−4x3 − 9x2 − 27x − 82) −
246
x−3
3. Perform the indicated operation and simplify your answer:
1
3
a. 2
−
x − 5x + 6 x − 2
10 − 3x
Ans:
(x − 2)(x − 3)
4
x+1
b.
−
x−3 3−x
x+5
Ans:
x−3
2x
4
c.
+
x+2 x+2
Ans: 2
3
x−2
d.
−
2
6x − 4x 9x − 6
−2x2 + 4x + 9
Ans:
6x(3x − 2)
x2
x2
e.
+
x−3 3−x
Ans: 0
4. Solve the equation. Be sure to check for extraneous solution:
7
a. + x = −8
x
Ans: {−7, −1}
1
2
x
b.
+ =
x−1 x x−1
Ans: {2}
2
4
c.
+ =2
x−2 x
Ans: {1, 4}
1
2
11
d.
−
= 2
x−2 x+3 x +x−6
Ans: {−4}
1
1
1
e.
−
=
2x − 4 2 − x 4
Ans: {8}
3
1
f.
= 2
x+1 x −1
4
Ans:
3
2
1
4x
+
=
g. 2
x − 25 x − 5 x + 5
Ans: {−3}
2
3
1
+
=
+1
h.
x+1 x−1 x+1
n √ √ o
Ans: − 5, 5