1. 9-6 Solving Rational Equations
3/27/17

2. To solve a rational EQ with a fraction on each side, cross-multiply to eliminate the fractions.
Then solve the resulting EQ, but be sure to check for extraneous solutions. 4 x =
2x – 3 5
20 =
2x2 – 3x
0 =
2x2 – 3x – 20
0 =
(2x + 5)(x – 4)
x =
-5/2 or 4

3. Combine fractions on one side 1st if you need to.5 2 1 5 – = + 2x 3 x 6 15 4x 6 5x – = + 6x 6x 6x 6x
Hey! The denom’s are all the same.. We can just ignore them and focus on the numerators!
This is because we could multiply both sides by 6x, and this would clear all fractions.
Just note that even if the “solution” is x = 0, it is NOT!
x can not equal 0 because it is restricted.

4. TIP: Get an LCD for the whole problem, not just each side
TIP: Get an LCD for the whole problem, not just each side. Then solve the EQ left by the numerators. 5 2 1 5 – = + 2x 3 x 6 15 4x 6 5x – = + 6x 6x 6x 6x
15 – 4x = 6 + 5x
15 = 6 + 9x
9 = 9x
x = 1

5. Bob can drywall the room in 6 hours.
Phil can drywall the room in 4 hours.
Together they can drywall the room in ____ hours.
h = # of hours
How much of the room can Bob do in 1 hour?
1/6 of it
How much of the room can Phil do in 1 hour?
1/4 of it
What is their rate working together?
(1/6 + 1/4)
Equation: (1/6 + 1/4)h = 1
(5/12)h = 1
h = 12/5 = 2.4 hours

6. Assignment:
Page 514 #1 – 5, 12 – 16, 24