I got here up with an answer of 7x^2-3/(x-3)(x+3)(x+2) and my TI 89 consents with my answer. First locate the liquid crystal reveal that's (x-3)(x+3)(x+2) x^2-9 is a distinction of two squares that are (x-3)(x+3) so now you've 4x/(x-3)(x+3) because the first portion of the priority.The denominator of the second one portion of the priority is a polynomial which will be factored into (x+3)(x+2). So now with the second one portion of the priority you've 3x+a million(x+3)(x+2) you presently prefer to position your liquid crystal reveal below the 4x and multiply it by the (x+2) that's lacking. next take the 3x+a million and position the liquid crystal reveal below it and multiply the numerator by the lacking portion of the liquid crystal reveal that's (x-3). Now your situation ought to look as if 4x(x+2) + (3x+a million)(x-3) all divided by the liquid crystal reveal of (x-3)(x+3)(x+2). next use the distributive sources for the first numerator and FOIL the second one numerator and receive (4x^2 + 8x) + (3x^2 -9x + x -3) all divided by the liquid crystal reveal of (x-3)(x+3)(x+2). next distribute the middle + time period and get 4x^2 + 8x + 3x^2 - 9x + x - 3. combine like words and get 4x^2 + 8x + 3x^2 - 8x -3. The 8x's cancel out and the x^2's combine to grant you 7x^2 - 3 all divided by the liquid crystal reveal of (x-3)(x+3)(x+2)
Comments
a) -1/11
b) ???
c) -2 root 80
d) 6
e) 5 root 17
f) 6
g) -3 root 21
1. -√(1/121)
121 = 11², so this is -√(1/11²) = -√(1/11)² = -1/11.
2. √50/9
50 = 25*2 = 5²*2, and 9 = 3², so this is √((5²*2)/(3²)) = (5/3)√2.
(This assumes that the positive root is the default. In full, it's ±(5/3)√2.)
3. -2√10*√8
√10*√8 = √80. 80 = 16*5 = 4²*5, so this is -2√(4²*5) = -2*4√5 = -8√5.
4. √288 ÷ √8
288÷8 = 36, so √288 ÷ √8 = √(288/8) = √36 = 6.
(This assumes that the positive root is the default. In full, it's ±6.)
5. √85*√5
85 = 17*5, so this is √(85*5) = √(17*5*5) = √(17*5²) = 5√17.
(This assumes that the positive root is the default. In full, it's ±5√17.)
6. 2√126÷√14,
126÷14 = 9, so this is 2√(126÷14) = 2√9 = 2*3 = 6.
(This assumes that the positive root is the default. In full, it's ±6.)
7. -√189.
189 = 11², so this is -√(11²) = -11.
sqrt(1/121) = sqrt(1^2 / 11^2) = sqrt(1/11)^2 = 1/11
sqrt(50/9) = sqrt(2 * 5^2/3^2) = sqrt(2 * (5/3)^2) = sqrt(2) * 5/3
-2*sqrt(10) * sqrt(8) = -2 * sqrt(80) = -2 * sqrt(16 * 5) = -8 * sqrt(5)
All of the others use similar techniques.
I got here up with an answer of 7x^2-3/(x-3)(x+3)(x+2) and my TI 89 consents with my answer. First locate the liquid crystal reveal that's (x-3)(x+3)(x+2) x^2-9 is a distinction of two squares that are (x-3)(x+3) so now you've 4x/(x-3)(x+3) because the first portion of the priority.The denominator of the second one portion of the priority is a polynomial which will be factored into (x+3)(x+2). So now with the second one portion of the priority you've 3x+a million(x+3)(x+2) you presently prefer to position your liquid crystal reveal below the 4x and multiply it by the (x+2) that's lacking. next take the 3x+a million and position the liquid crystal reveal below it and multiply the numerator by the lacking portion of the liquid crystal reveal that's (x-3). Now your situation ought to look as if 4x(x+2) + (3x+a million)(x-3) all divided by the liquid crystal reveal of (x-3)(x+3)(x+2). next use the distributive sources for the first numerator and FOIL the second one numerator and receive (4x^2 + 8x) + (3x^2 -9x + x -3) all divided by the liquid crystal reveal of (x-3)(x+3)(x+2). next distribute the middle + time period and get 4x^2 + 8x + 3x^2 - 9x + x - 3. combine like words and get 4x^2 + 8x + 3x^2 - 8x -3. The 8x's cancel out and the x^2's combine to grant you 7x^2 - 3 all divided by the liquid crystal reveal of (x-3)(x+3)(x+2)