Odpowiedź:
Zadanie 4
Przykłady a,b,c,d w załącznikach
Koncówka przykładu d:
(x+2)(x-5)/(x+2)(2x-1)=0
x-5/2x-1=0 /*(2x-1)
x-5=0
x= 5
e) 2x+1/x+1=4x+2/5x-1
D: x+1≠0 5x-1≠0
x≠-1 5x≠1/:5
x≠ 1/5
(2x+1)(5x-1)=(4x+2)(x+1)
(2x+1)(5x-1) - (4x+2)(x+1) =0
10x²-2x+5x-1-(4x²+4x+2)=0
10x²-2x+5x-1-4x²-4x-2=0
6x²-3x-3=0/:3
2x²-x-1=0
2x²-x-2x-1=0
x(2x+1)-2(x+1)=0
(2x+1)(x-1)=0
2x+1=0 x-1=0
2x= 1/:2 x= 1
x= 1/2
f) x+2/x+4 - 8/x²+4x =0
D: x²+4x≠0
x(x+4)≠0
x≠0 x+4≠0
x≠ -4
x+2/x+4 - 8/x(x+4)=0
x(x+2)/x(x+4) -8/x(x+4) =0
x(x+2)-8/x(x+4)=0
x²+2x-8/x(x+4)=0
x²+4x-2x-8/x(x+4)=0
x(x+4)-2(x+4)/x(x+4)=0
(x+4)(x-2)/x(x+4)=0
x-2/x=0 /*x
x-2=0
x= 2
g) D: x-5≠0 x+1≠0
x≠ 5 x≠ -1
x²-4x+31/x²-4x-5 = x+1/x-5 - x-5/x+1
x²-4x+31/x²-4x-5 - x+1/x-5+ x-5/x+1 =0
x²-4x+31/x²+x-5x-5 - x+1/x-5 + x-5/x+1=0
x²-4x+31/(x+1)(x-5) - (x+1)(x+1)/(x+1)(x-5) + (x-5)(x-5)/(x-5)(x+1)=0
x²-4x+31/(x+1)(x-5) - (x+1)²/(x+1)(x-5)+ (x-5)²/(x-1)(x-5)=0
x²-4x+31-(x²+2x+1)+x²-10x+25/(x+1)(x-5)=0
x²-4x+31-x²-2x-1+x²-10x+25/(x+1)(x-5)=0
x²-16x+55/(x-1)(x-5)=0
x²-5x-11x+55/(x+1)(x-5)=0
x(x-5)-11(x-5)/(x+1)(x-5)=0
(x-5)(x-11)/(x+1)(x-5)=0
x-11/x+1=0/*(x+1)
x-11=0
x= 11
h) D: x²-6x≠0
x(x-6)≠0
x≠0 x-6≠0
x≠6
x-3/x - 18/x²-6x=0
x-3/x - 18/x(x-6)=0
(x-6)(x-3)/x(x-6) - 18/x(x-6)=0
(x-6)(x-3)-18/x(x-6)=0
x²-3x-6x+18-18/x(x-6)=0
x²-9x/x(x-6)=0
x(x-9)/x(x-6)=0 /*(x-6)
x-9=0
x= 9
