1. EQUATIONS & INEQUALITIES
SOLVING RATIONAL
EQUATIONS & INEQUALITIES
#1 - Set up proportion and solve
#2 - Multiply by LCD of all terms and solve
METHOD 1: PROPORTION– combine fractions each side
EX #1)
Cross multiply

2. Method 1: Proportion PRACTICE
EX #3)
EX #2)

3. Method 1: Proportion PRACTICE
EX #4)
Methods for Solving Quadratic: Factoring, Quadratic Formula, Completing the Square

4. METHOD 2 - MULTIPLY BY LCD
“Cancels out all fractions to make normal equation to solve”
Example 1 Basic Rational Equations
20x a) b)
14y
8 – 30 = 200x
35 – 8y = 21y
– 22 = 200x
35 = 29y
x = – 11/100
y = 35/29

5. Method 2: LCD PRACTICE 24(3 – x) 5(3 – x) + 2(24) = 6(3 – x)

6. Extraneous Solutions: algebraic solution creates a zero denominator in original
(x + 1)(x – 1)
EX 1)
(x + 1)(x – 1)
x = -1 is extraneous because

7. EX 2) x2 – 7 + x(x2 – 1) = (x – 1)(x2 – x + 1)
x2 – 7 + x3 – x = x3 – x2 + x – x2 + x – 1
x2– x – 7 = – 2x2 + 2x – 1
3x2– 3x – 6 = 0
x2– x – 2 = 0
(x – 2)(x + 1) = 0
x = x = – 1

8. PRACTICE: Solving RATIONAL INEQUALITIES
(1) Find any excluded values. (2) Solve as a rational equation.
(3) Test values on different domains between excluded and solution values to solve.
EX #2)
EX #1)
EX #3)