1. Chapter 9 Remediation Study Guide due Wednesday –
25 points for completed review sheet AND remediation forms

2. 9.1 Multiplying and Dividing Rational Expressions #1-6
IDENTIFICATION
1) Fractions that are multiplied or divided
2) There is NO “=” sign and NO inequality sign
FINAL PRODUCT
1) One fraction
2) Completely factored
3) Completely simplified

3. 9.1 Multiplying and Dividing Rational Expressions #1-6
PROCESS
1) Change division problems to multiplication
2) Factor numerators AND factor denominators
3) Cancel like factors (only numerators and
denominators cancel)
4) Multiply numerators AND multiply denominators

4. Example Method 1: Cancel first 3 6
**IF YOU HAVE TROUBLE CANCELING FIRST…TRY THIS METHOD

5. Example
Method 2: Multiply first 18

6. 9.2 ADDING AND SUBTRACTING RATIONAL EXPRESSIONS #7-12
IDENTIFICATION
1) Fractions separated by “+” or “─”
2) There is NO “=” sign and NO inequality sign
FINAL PRODUCT
1) One fraction
2) Completely factored
3) Completely simplified

7. 9.2 ADDING AND SUBTRACTING RATIONAL EXPRESSIONS #7-12
PROCESS
1) Rewrite as fractions if necessary
2) Identify LCM of denominators
3) Rewrite EACH fraction as equivalent fraction
with LCM as denominator
4) Add or subtract fractions (+ or – numerators,
keep denominator)

8. Example Method 1: 2mn 3mm 2.3mnn LCM: 2.3mmnn=6m2n2
**If you have problems writing equivalent
fractions…try the next method
LCM: 2.3mmnn=6m2n2

9. Example
Method 2:
(LCM: 6m2n2)

10. 9.3 Solving Rational Equations #13-18
IDENTIFICATION
1) Fractions separated by “+” or “─”
2) There IS an “=” sign.
FINAL PRODUCT
1) Number(s) –or-
2) Infinite solutions –or-
3) No solutions –or-

11. 9.3 Solving Rational Equations #13-18
PROCESS
1) Identify LCM of denominators
2) Multiply ENTIRE equation by LCM
(denominators will cancel)
3) Solve for variable
4) Check quadratic equations for extraneous solutions

12. Example
LCM
Method 1:

13. Example
LCM
Method 2:

14. 9.3 Solving Rational Inequalities #19-20
IDENTIFICATION
1) Fractions separated by “+” or “─”
2) There IS an inequality sign.
FINAL PRODUCT
1) An inequality –or-
2) Infinite solutions –or-
3) No solutions –or-

15. 9.3 Solving Rational Inequalities #19-20
PROCESS
1) Find excluded values
2) Solve related equation
3) Use values in step 1 and step 2 to divide a number
line into regions. Test a value in each region to
determine which regions satisfy the original
inequality.

16. Example EV
LCM