Practice 9-6
Solve. Make sure to check for extraneous solutions.
1.
12
𝑥
3
3
4.
𝑥
𝑥+2
+𝑥 =
7.
4
𝑥−2
= 𝑥+3
+4 = 2
5𝑥+8
𝑥+2
−1
2𝑥
𝑥−3
10. 𝑥 + 𝑥−1 = 1 − 𝑥−1
13. 3 =
6𝑥−1
2𝑥+7
+
22
𝑥+5
2.
𝑥
𝑥−1
𝑥
5.
1
5
+𝑥
3𝑥−2
8.
4
5𝑥
−1 = 2
1
=0
3
+ 10 = 2𝑥
11. 5 −
3𝑥+2
𝑥−1
3.
𝑥+10
𝑥 2 −2
=𝑥
6.
1
2𝑥
5
9.
=
2𝑥−4
𝑥+2
14.
4𝑥
5𝑥
−
𝑥−1
𝑥−2
=
2
𝑥 2 −3𝑥+2
3
+ 𝑥 = 𝑥−1
6
𝑥−1
12.
4
4
2
= 𝑥−2 + 𝑥+1
𝑥+1
𝑥−3
12
= 4 − 𝑥 2 −2𝑥−3
Review.
Add or Subtract.
15.
4
9
+
𝑥−3
𝑥−5
16.
5
6𝑥𝑦
−
7
8𝑥
17.
2𝑥−3
𝑥 2 −5𝑥+6
−
5
𝑥 2 −9
Multiply or divide.
18.
6𝑥+12 10
∙ 𝑥+2
5
19.
𝑦
𝑥 2 −𝑦2
÷
𝑦2
𝑥−𝑦
20.
3𝑚2 −75
6𝑚2 +30𝑚
4𝑚−20
9𝑚2 +45𝑚
State the following for each rational equation.
3
4𝑥−3
21. 𝑓(𝑥) = 𝑥−6 − 5
Domain:
22. 𝑓(𝑥) = 8𝑥+2
Range:
Domain:
Range:
Equation for the vertical asymptote:
Equation for the vertical asymptote:
Equation for the horizontal asymptote:
Equation for the horizontal asymptote: