1a. [(a²+6a-2a+4)/(a+6)]:[a(a+2)/(a-6)(a+6)] +12/a =
= (a+2)²/(a+6) : [a(a+2)/(a-6)(a+6)] +12/a =
= [(a+2)²(a-6)(a+6)]/[a(a+2)(a+6)] +12/a =
=(a+2)(a-6)/a +12/a = (a²+2a-6a-12+12)/a=
=(a²-4a)/a = a-4
1b. 2x/(x-1)(x+1) : [1/(x+1)² +1/(x-1)(x+1)]=
= 2x/(x-1)(x+1) : [(x-1+x+1)/(x+1)²(x-1)]=
=[2x(x+1)²(x-1)]/[(x-1)(x+1)·2x] =(x+1)
2a. 2x²+x-14x-7 = 9x²-6x+1 - 50
7x²+7x - 42 =0
x² +x -6 = 0
x1= -3 ; x2=2
2b. [(4x-3)(x-1) - x]/x(x-1) = (2x+3)/x(x-1)
x≠0 ; x≠1
(4x²-3x-4x+3) = 2x+3
4x² - 9x =0
x≠0 ⇒ 2x - 9 = 0
x = 4,5
3. I - x g. ⇒ za 1g napolnitsa 1/x
II (x-24)g. ⇒ 1/(x-24)
⇒ I rabotal 28g. a II 20g. ⇒
28/x + 20/(x-24) = 2/3
x² - 96 +1008 =0
x1 = 12 ne udovl, t.k. x-24<0 <br> x= 84 g.
Otvet; I - 84g. ; II - 60g.
4a. 3√12 +2√16 - √64 - √(9·12) = 3√12 + 8 -8 -3√12 =0
4b. 4√(2/5·10)+1/3·√900- 6√1 = 8+1/2·30 -6= 17
4c. [(√7+√2)² +(√7-√2)²]/(√7-√2)(√7+√2) =
=(7+2√14+2 +7-2√14+2)/(7-2) =
= 18/5 = 3,6