course Mth 158
Some of this I had some trouble with.. a few that I am not too sure about are #'s 16,22,46,52,64, and defenitly 70
R.71.When the numerator and denominator of a rational expression contain no common factors (except 1 and ?), the rational expression is in .. lowest term.
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4. true of False: The LCM of 2x^3+6x^2 and 6x^4+4x^3 is 4x^3(x+1)?False
Reduce each rational expression to lowest terms.
7.x^2-2x over 3x-6= x(x-2) over 3(x-2)= x over 3
10. x^2+4x+4 over x^2-16= (x+2) (x+2) over (x+4) (x-4) = (x+2) (x+2) over (x+2) (x-2)= (x+2) over (x-2)
13. x^2+4x-5 over x^2-2x+1= (x+5) (x-1) over (x-1) (x-1)= (x+5) over (x-1)
16.2x^2+5x-3 over 1-2x= x(2x+5)-3 over 1-2x
The numerator factors into (x + 3)·(2·x - 1). The denominator could be written as -(2x - 1). So the result is - (x + 3).
When you have a question on a specific problem, be sure you include the details of the steps. I can't tell from your result how you obtained it.
Perform the indicated operation and simplify the result. Leave your answer in factored form.
19. 4x^2 over x^2-16 * x-4 over 2x= 4x^2 over (x-4) (x+4) * x-4 over 2x= 2x over x+4
22. 6x-27 over 5x * 2 over 4x-18= 3(2x-9) over 5x * 2 over 2(2x-9)= 3 over 5x
I can't tell if this is 6x-27 over (5x * 2) over 4x-18 or (6x-27 over 5x) * (2 over 4x-18); if the latter then your solution is good.
25.6x / x^2-4 over 3x-9 / 2x+4= 6x over x^2-4 * 2x+4 over 3x-9= 6x over (x-2) (x+2) * 2(x+2) over 3(x-3)= 4x over (x-2) (x-3)
28. x-2 / 4x over x^2-4x+4 / 12x= x-2 over 4x * 12x over x^2-4x+4 = x-2 over 4x * 12x over (x-2) (x-2)= 12x over 4x(x-2)= 3x over x-2
31. x^2+7x+12 / x^2-7x+12 over x^2+x-12 / x^2-x-12= x^2+7x+12 over x^2-7x+12 * x^2-x-12 over x^2+x-12= (x+4) (x+3) over (x-4) (x-3) * (x-4) (x+3) over (x+4) (x-3)= (x+3)^2 over (x-3)^2
34.9x^2+3x-2 / 12x^2+5x-2 over 9x^2-6x+1 / 8x^2-10x-3= 9x^2+3x-2 over 12x^2+5x-2 * 8x^2-10x-3 over 9x^2-6x+1= (3x-1) (3x+2) over (4x-1) (3x+2) * (4x+1) (2x-3) over (3x-1) (3x-1)= (4x+1) (2x-3) over (4x-1) (3x-1)
Perform the indicated operation and simplify the result. Leave your answer in factored form.
37. x^2 over 2x-3 ?4 over 2x-3= x^2-4 over 2x-3= (x+2) (x-2) over 2x-3
40. 2x-5 over 3x+2 + x+4 over 3x+2= 2x-5+x+4 over 3x+2= 3x-1 over 3x+2
43. 4 over x-2 + x over 2-x= 4 over x-2 ?x over x-2= 4-x over x-2
46. 2 over x+5 ?5 over x-5= 2 over x+5 * x-5 over x-5 ?x+5 over x+5 * 5 over x-5= 2x-10-5x+25 over x^2-25-x^2-25= -3x+15
I can't read the problem in this notation. Can you submit it in standard typewriter notation?
49. x-3 over x+2 ?x+4 over x-2= x-3 over x+2 * x-2 over x-2 ?x+2 over x+2 * x+4 over x-2= x^2-2x-3x+6-(x^2+4x+2x+8) over (x+2) (x-2)= -11x-2 over (x+2) (x-2)
52.x-1 over x^3 + x over x^2+1= x-1 over x^3 * x^2+1 over x^2+1 + x^3 over x^3 * x over x^2+1= (x^3+1x-x^2-1)+x^4 over (x^5+x^3) + (x^5+x^3)
Find the LCM of the given polynomials.
55. x^3-x, x^2-x?x^3-x= x(x^2-1)= x(x-1) (x+1)?.x^2-x=x(x-1)?LCM is x(x+1) (x-1)
58. x-3, x^2+3x, x^3-9x?x-3=x-3?x^2+3x=x(x+3)?^3-9x= x(x^2-9=x(x-3) (x+3).. LCM is x(x-3) (x+3)
Perform the indicated operation and simplify the result. Leave your answer in factored form.
61. x over x^2-7x+6 ?x over x^2-2x-24= x over x^2-7x+6 * x^2-2x-24 over x^2-2x-24 ?x^2-7x+6 over x^2-7x+6 * x over x^2-2x-24= x over (x-6) (x-1) * (x-6) (x+4) over (x-6) (x+4) ?(x-6) (x-1) over (x-6) (x-1)* x over (x-6) (x+4)= x(x+4) over (x-6) (x-1) (x+4)- x(x-1) over (x-6) (x-1) (6+4)= x^2+4x-x^2+x over (x-6) (x+4) (x-1)= 5x over (x-6) (x+4) (x-1)
64. 3x over x-1 ?x-4 over x^2-2x+1= 3x over x-1 * (x-1) (x-1) over (x-1) (x-1) ?x-4 over (x-1) (x-1) * x-1 over x-1 = 3x(x-1) over (x-1) (x-1) ?x-1 (x-1) over (x-1)= 3x^2-3x-x+1-x+1 over x-1= 3x^2-5x+2 over x-1
67. x+4 over x^2-x-2 ?2x+3 over x^2 +2x-8 = x+4 over (x-2) (x+1) ?2x+3 over (x+4) (x-2)= (x+4) (x+4) over (x-2) (x+1) (x+4) ?(2x+3) (x+1) over (x+4) (x-2) (x+1)= x^2 +8x+16-(2x^2+5x+3) over (x-2) (x+1) (x+4) = -x^2+3x+13 over (x-2) (x+1) (x+4)
**70. x over (x-1)^2 + 2 over x ?x+1 over x^3-x^2= x over (x-1) (x-1) + 2 over x ?(x+1) over x^2(x-1) = x over (x-1) (x-1) * x over x + 2 over x * (x-1) (x-1)- (x+1) over x^2 (x-1) * x over x= 2-(x+1)*x over (x-1)^3 x^2+x = -2x+2 *x over (x-1)^3 x^2+x= -2x^2+2x over (x-1)^3 x^2+x
I've responded on a couple of your problems, but I need to see most of the subsequent in standard typewriter notation with proper grouping of numerators and denominators, using / instead of 'over', etc..