6/(x-1)(x+3)-24/(x-2)(x+4)=1

решение 6/(x-1) *(x+3) - 24/(x-2)*(x+4) =1 . 6/x^2+2x-3 - 24/ x^2+2x-8 =1 .

пусть

x≠1;x≠-3;x≠2;x≠-46/(x²+2x-3) -24/(x²+2x-8)=1a=x²+2x-36/a-24/(a-5)=1a(a-5)-6(a-5)+24a=0a²-5a-6a+30+24a=0a²+13a+30=0a1+a2=13 U a1*a2=30a1=3⇒x²+2x-3=3x²+2x-6=0D=4+24=28x1=(-2-2√7)/2=-1-√7 U x2=-1+√7a2=10⇒x²+2x-3=10x²+2x-13=0D=4+52=56x3=(-2-2√14)/2=-1-√14 U x4=-1+√14