Bell Assignment Find the common denominator.

1 + 3 - 6x x-2 x+2 x2 – 4

(x+2)(x-2)

Rational EquationsObjective: Be able to solve equations

involving rational expressions.

Strategy: Multiply by the common denominator.

NOTE: BE SURE TO CHECK FOR EXTRANEOUS SOLUTIONS!!

Example 1: Solve. x + 3x = 2 3 4

Find the common denominator12

Multiply by the common denominator.

12 12 12

Simplify the fractions. 4x + 3(3x) = 2(12)

4x + 9x = 24Solve the equation.

13 x = 24 x = 24 13

Check your solution!!

Example 2: Solve. 1 + 3 = 4 x-2 x+3 x2+x-6

Common Denominator: (x+3)(x-2)

1(x+3) + 3(x-2) = 4 x + 3 + 3x – 6 = 4 4x – 3 = 4 x = 7 4

BE SURE TO CHECK ANSWERS!!

Example 3: Solve x - x+3 = 5 4 2

Common Denominator: 4

x – 2(x+3) = 4(5)x – 2x – 6 = 20-x – 6 = 20

x = -26

BE SURE TO CHECK ANSWERS!!

Example 4: Solve. 2 = 4 + 3x x + 3 x2 – 9 x – 3

Common Denominator: (x+3)(x-3)

2(x-3) = 4 + 3x(x+3)

2x – 6 = 4 + 3x2 + 9x 3x2 + 7x +10 = 0x = -7 ± i√71 6

BE SURE TO CHECK YOUR ANSWERS!!

Example 5: Solve. 2 + 3 = 2 x x – 1

Common Denominator: x ( x-1)

2(x -1) + 3(x) = 2x (x – 1) 2x – 2 + 3x = 2x2 – 2x5x – 2 = 2x2 – 2x 2x2 – 7x + 2 = 0

7 ± √33 4

BE SURE TO CHECK ANSWERS!!

Example 6:Solve. 1 + 3 = 6x x – 2 x + 2 x2 – 4

Common Denominator: (x+2) ( x- 2)

1(x+2) + 3(x – 2) = 6xx + 2 + 3x – 6 = 6x4x – 4 = 6xx = -2 NO SOLUTION!!

BE SURE TO CHECK YOUR ANSWERS!

Example 7: Solve. 6 + 5x+6 = 100 – 4x 4 3

Common Denominator: 12

6(12) + 3(5x+6) = 4(100 – 4x) 72 + 15x + 18 = 400 – 16x 90 + 15 x = 400 – 16x 31x = 310 x = 10

BE SURE TO CHECK ANSWERS!!

EXIT PASS1. 2 = 3 - 1 x x – 2

2. 3 + 4 = 1 x2 - 3x x x – 3

X = 4; X = -1

X = 3