Math Algebra Review Answer Key

12.4-12.6 Review Algebra 1 CP Name: KEY Hour: State the excluded values of the rational expression. 1. 5 / (x + 3) x + 3 = 0 x = -3 2. 5x / (2x + 7) 2x + 7 = 0 2x = -7 x = -7/2 3. (x + 8) / (x² - 4) (x + 2)(x - 2) = 0 x = -2, 2 4. 7 / (x² + 14x - 15) (x + 15)(x - 1) = 0 x = -15, 1 For #5-20, simplify the expression. 5. (4x²)/(6x²) = (2/3)x^(2-2) = 2/3 6. (x²)/(4x²) = 1/4 7. (2x³)/(8x²) = (1/4)x^(3-2) = x/4 8. (3x - 15)/(4x - 20) = 3(x - 5) / 4(x - 5) = 3/4 9. (6x + 24)/(6x) = 6(x + 4) / 6x = (x + 4) / x 10. (2x - 8)/(3x - 12) = 2(x - 4) / 3(x - 4) = 2/3 11. (6x³ - 18x²)/(3x² - 9x) = 6x²(x - 3) / 3x(x - 3) = 6x²/3x = 2x 12. (4x³ - x²)/(5x² - 3x) = x²(4x - 1) / x(5x - 3) = (x(4x - 1)) / (5x - 3) 13. (x + 3)/(x² - 9) = (x + 3) / ((x + 3)(x - 3)) = 1 / (x - 3) 14. (x² - 16)/(x² - 11x + 28) = (x + 4)(x - 4) / ((x - 4)(x - 7)) = (x + 4) / (x - 7) 15. (x² - 7x + 10)/(x² - 2x - 15) = (x - 5)(x - 2) / ((x - 5)(x + 3)) = (x - 2) / (x + 3) 16. (2x - 14)/(x² - 9x + 14) = 2(x - 7) / ((x - 7)(x - 2)) = 2 / (x - 2) 17. (3 - x) / (x² + 5x - 24) = -(x - 3) / ((x + 8)(x - 3)) = -1 / (x + 8) 18. (x² - 3x - 10) / (x² + 5x + 6) = (x - 5)(x + 2) / (x + 2)(x + 3) = (x - 5) / (x + 3) 19. (x² - 3x - 10) / (3x² + 6x) = (x - 5)(x + 2) / 3x(x + 2) = (x - 5) / 3x 20. (x² + 3x - 4) / (3x² - 5x + 2) = (x + 4)(x - 1) / (3x - 2)(x - 1) = (x + 4) / (3x - 2) Find the product, then simplify. 21. (x² + 11x + 5) / (5x²) * (10x) / (x² + x - 1) = (2x + 1) / x 22. (x² + 7x) / (7x²) * (7x²) / (x + 7) = 7x / 7 = x 23. (x - 3) / (2x + 3) * (x + 4) / (x² + 2x - 15) = (x - 3) / (2x + 3) * (x + 4) / ((x + 5)(x - 3)) = 1 / 2(x + 5) 24. (3x - 9) / (x² - 9x + 20) * (x² - 16) / (x² - 3x) = 3(x - 3) / (x - 5)(x - 4) * (x - 4)(x + 4) / x(x - 3) = 3(x + 4) / x(x - 5) 25. (x² + 2x - 3) / (x² - 6) * (x - 3) / (x + 1) = (x + 3)(x - 1) / (x² - 6) * (x - 3) / (x + 1) = (x - 3)² / (x² - 6) 26. (x - 1) / (x + 1) * (x + 1) / (1 - x) = (x - 1) / (1 - x) = -1 27. (x² + 4x + 4) / (x² + 6x + 8) * (x² + 5x + 6) / (x² + 7x + 12) = (x + 2)(x + 2) / (x + 4)(x + 2) * (x + 3)(x + 2) / (x + 4)(x + 3) = (x + 2) / (x + 4) 28. (x² + 7x - 21) / (x² + 4x - 21) * (x² - 3x - 10) / (x² - 7x + 12) = (x + 7)(x - 3) / (x + 7)(x - 3) * (x - 5)(x + 2) / (x - 4)(x - 3) = (x - 5)(x + 2) / (x - 4)(x - 3) 29. (x² + 4x - 12) / (6x² + 16) * (6x + 16) / (x² + x - 2) = (x + 6)(x - 2) / 2(3x + 8) * 2(3x + 8) / (x + 2)(x - 1) = (x + 6) / (x - 1) Find the quotient, then simplify. 30. (11x⁴)/(18) ÷ (22)/(9x²) = (11x⁴)/(18) * (9x²)/(22) = (11x⁶)/(36) = (x⁶)/(4) 31. (24)/(5x³) ÷ (6)/(25x²) = (24)/(5x³) * (25x²)/(6) = (20x²)/(x³) = 20/x 32. (2x + 10)/(x² - 25) ÷ (4x²)/(2x² - 10x) = (2(x + 5))/((x + 5)(x - 5)) * (2x(x - 5))/(4x²) = 1/x Find the sum or difference. Simplify your answers. 36. (3x)/(x²) + (4)/(x²) = (3x + 4)/(x²) = (3 + 4/x)/x 37. (3x)/(7) + (4)/(7) = (3x + 4)/(7) 38. (x²)/(5x) - (4)/(5x) = (x² - 4)/(5x) = (x - 2)(x + 2)/(5x) 39. (5x + 2)/(x - 2) - (2x - 4)/(x - 2) = (5x + 2 - 2x + 4)/(x - 2) = (3x + 6)/(x - 2) = 3(x + 2)/(x - 2) 40. (x + 3)/(2x) - (5x + 3)/(2x) = (x + 3 - 5x - 3)/(2x) = -4x/(2x) = -2 41. (6x - 1)/(x + 1) + (3x - 5)/(x + 1) = (9x - 6)/(x + 1) = 3(3x - 2)/(x + 1) Find the LCD, then find the sum or difference. Simplify your answers if possible. 42. (2x)/(5x) + (3x)/(5x) = (5x)/(5x) = 1 43. (7x)/(21x) + (12x)/(21x) = (19x)/(21x) = 19/21 44. (9x²)/(18x²) + (3x)/(18x²) = (9x² + 3x)/(18x²) = (3x(3x + 1))/(18x²) = (3x + 1)/(6x) 45. (2f²)/(2f³) + (h)/(2f³) = (2f² + h)/(2f³) 46. (4m)/(10m²) + (2)/(10m²) = (4m + 2)/(10m²) = (2m + 1)/(5m²) 47. (6x³)/(15x³) + (4x)/(15x³) = (10x³)/(15x³) = 2/3 48. (2)/(3x) + (4x)/(3x) = (2 + 4x)/(3x) or (4x + 2)/(3x) 49. (y²)/(6x²) + (20xy)/(6x²) = (y² + 20xy)/(6x²) 50. (3x)/(21x³) - (3a)/(21x³) = (3x - 3a)/(21x³) = (x - a)/(7x²)