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

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

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

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

Example Method 2: Multiply first 18

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

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)

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

Example Method 2: (LCM: 6m2n2)

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-

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

Example LCM Method 1:

Example LCM Method 2:

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-

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.

Example EV LCM