Mnożysz wyrazy skrajne i przyrównujesz to iloczynu wyrazów środkowych [latex]6x=10 \ x= frac{10}{6} = frac{5}{3} [/latex] [latex]4x=2x+2 \ 2x=2 \ x=1[/latex] [latex]10x-10=3x+6 \ 7x=16 \ x= frac{16}{7} = 2 frac{2}{7} [/latex] [latex] x^{2} -1 = x^{2} +3x \ 3x=-1 \ x=- frac{1}{3} [/latex] [latex]2 a^{2} -a-1=2 a^{2} +6a \ -7a=1 \ a=- frac{1}{7} [/latex] [latex]b^{2} -5b+6= b^{2} +b \ -6b=-6 \ b=1[/latex]
a) x/2=5/6 /*6 3x=5 /:5 x=5/3 x=1²/₃ b) x/2=(x+1)/4 /*4 2x=x+1 2x-x=1 x=1 c) 2(x-1)/3=(x+2)/5 /*15 5*2(x-1)=3(x+2) 10x-10=3x+6 10x-3x=6+10 7x=16 x=16/7 x=2²/₇ d) (x-1)/(x+3)=x/(x+1) /*(x+3)(x+1), x≠-3 i x≠-1 (x-1)(x+1)=x(x+3) x²-1=x²+3x 3x=-1 /:3 x=-1/3 e) (2a+1)/(2a)=(a+3)/(a-1) /*2a(a-1) , a≠0 i a≠1 (2a+1)(a-1)=2a(a+3) 2a²-2a+a-1=2a²+6a -a-6a=1 -7a=1 a=-1/7 f) (b-2)/(b+1)=b/(b-3) /*(b+1)(b-3) , b≠-1 i b≠3 (b-3)(b-2)=b(b+1) b²-2b-3b+6=b²+b -5b-b=-6 -6b=-6 /:(-6) b=1
