Sarah Owens 1. When the numerator and denominator of a rational expresseioncontain no common factors (except 1 and -1), the rational expression is in Lowest Terms. 4. False. The LCM would be 6x^3(x+1). Reduce to Lowest terms 7. x^2-2x = x(x-2) = x _____________________ 3x-6 = 3(x-2) = 3 10. x^2+4x=4 = (x-4)(x+16) = (x+2) __________ _____________ ________ x^2 - 16 (x+16)^2 (x+4) 13. x^2+4x-5 = (x+5)(x-1) =(x+5) __________________________________ x^2-2x+1 (x-1)^2 (x-1) 16. 2x^2+5x-3 ?? ___________ 1-2x Perform indicated operation and simplify the result. 19. 4x^2 times x-4 4x^2 times x-4 2x _____ _____ = ______ _____ = ____ x^2-16 2x (x-4)(x+4) 2x x+4 22. ?? 25. 6x = 6x times 2x+4 = 6x times 2(x+2) = 4x _________ _______ _________ ___________ __________ ________ x^2 - 4 x^2 - 4 3x-9 (x-2)(x+2) 3(x-3) (x-2)(x-3) _____________ 3x - 9 ________ 2x + 4 28. ?? 31. x^2 + 7x + 12 = x^2 + 7x + 12 times x^2 - x - 12 = _______________ _______________ ______________ x^2 + 7x + 12 x^2 + 7x + 12 x^2 + x - 12 _______________________________________________________________ x^2 + x - 12 = (x+3)(x+4) times (x-4)(x+3) = = (x+3)^2 _______________ _____________ ______________ _________ x^2 - x - 12 = (x-3)(x-4) (x+4)(x-3) (x-3)^2 34. 9x^2 + 3x - 2 = (3x + 2) (3x - 1) __________________ ___________________ = (3x + 2)(3x - 1) times (4x+1)(2x-3) = (4x+1)(2x-3) 12x^2 + 5x - 2 (4x - 1) (3x +2) __________________ ______________ _____________ _______________________________________________ (4x-1)(3x+2) (3x-1)(2x-3) (4x-1)(3x-1) 9x^2 - 6x +1 (3x - 1) (3x - 1) _____________ ___________________ 8x^2 - 10x - 3 (4x + 1) (2x - 3) Perform operations and simplify. 37. x^2 - 4 = x^2 - 4 = (x+2)(x-2) _______ _______ __________ ______________ 2x - 3 2x - 3 2x - 3 2x - 3 40. 2x - 5 + x+4 = 2x - 5 = 4x _________ __________ _________ ________ 3x + 2 3x + 2 3x + 2 3x + 2