Question

separate 1/x(x+2) into partial fraction

Answer 1

=1/x(x+2)=a/x+b/(x+2). -(I)
cross multiplication
1=a(x+2) + bx

now put x=(-)2
so, 1=a(0) -2b
1=-2b

【b=-1/2】

now again put x=0 then
1=2a+b(0)
so 【a=1/2】

put value of a and b in equation (I).

then
【1/x(x+2)=1/2x - 1/2(x+2)】
transformation complete.