1. (x+2)(x-2)

2.  Objective: Be able to solve equations involving rational expressions.  Strategy: Multiply by the common denominator.  NOTE: BE SURE TO CHECK FOR EXTRANEOUS SOLUTIONS!!

3. x + 3x = 2 3 4 Find the common denominator 12 Multiply by the common denominator. 12 Simplify the fractions. 4x + 3(3x) = 2(12) 4x + 9x = 24 Solve the equation. 13 x = 24 x = 24 13 Check your solution!!

4. 1 + 3 = 4 x-2 x+3 x 2 +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!!

5. 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!!

6. 2 = 4 + 3x x + 3 x 2 – 9 x – 3 Common Denominator: (x+3)(x-3) 2(x-3) = 4 + 3x(x+3) 2x – 6 = 4 + 3x 2 + 9x 3x 2 + 7x +10 = 0 x = -7 ± i√71 6 BE SURE TO CHECK YOUR ANSWERS!!

7. 2 + 3 = 2 x x – 1 Common Denominator: x ( x-1) 2(x -1) + 3(x) = 2x (x – 1) 2x – 2 + 3x = 2x 2 – 2x 5x – 2 = 2x 2 – 2x 2x 2 – 7x + 2 = 0 7 ± √33 4 BE SURE TO CHECK ANSWERS!!

8. 1 + 3 = 6x x – 2 x + 2 x 2 – 4 Common Denominator: (x+2) ( x- 2) 1(x+2) + 3(x – 2) = 6x x + 2 + 3x – 6 = 6x 4x – 4 = 6x x = -2 NO SOLUTION!! BE SURE TO CHECK YOUR ANSWERS!

9. 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!!

10.  2 = 3 - 1 x x – 2  3 + 4 = 1 x 2 - 3x x x – 3 X = 4; X = -1 X = 3