1
1/(x-2)(x+2)=a/(x-2)+b/(x+2)
a(x+2)+b(x-2)=1
ax+2a+bx-2b=1
x*(a+b)+(2a-2b)=1
{a+b=0
{2(a-b)=1⇒a-b=1/2
прибавим
2a=1/2
a=1/4
1/4+b=0
b=-1/4
2
1/(x+1)(x²-x+1)=a/3(x+1)+(bx+2)/(x²-x+1)
a(x²-x+1)+(bx+2)*(x+1)=3
ax²-ax+a+bx²+2x+bx+2-3=0
x²*(a+b)-x(a-b-2)+(a-1)=0
{a-1=0⇒a=1
{a+b=0⇒b=-a⇒b=-1
{a-b=2
3
(2x-1)/(x²+1)(x+2)=a/(x+2)+bx/(x²+1)
a(x²+1)+bx*(a+2)=2x-1
ax²+a+bx²+2bx=2x-1
x²(a+b)+2bx+a=2x-1
{a=-1
{a+b=0⇒b=-a⇒b=1
{2b=2⇒b=1