partial fraction help

[nipuna92]

please anyone can do this
because i cannot remember

please try to include every step in your answer

[astarmathsandphysics]

I will answer this when my internet goes back up. There is some fault now and i am on a phone.

[nipuna92]

ok
no hurry take ur time.

[slvri]

ok.......so 100/(x²)(10-x) can be written in the form A/x²+B/x+C(10-x) where A, B and C are constants whose values are to be found
100/(x²)(10-x)=A/(x²)+B/x+C/(10-x)...........(X)
now the trick is first find the values of A and C by substituting an appropriate value of x, then find B by a algebraic method
to find A, first multiply every term of (X) by x²
100/(10-x)=A+Bx+Cx²/(10-x)
now put x=0
100/10=A+0+0
A=10
to find C, first multiply every term of (X) by (10-x)
100/(x²)=A(10-x)/(x²)+B(10-x)/x+C
now put x=10
1=0+0+C
C=1
now to find B first put values of A and C in (X)
100/(x²)(10-x)=10/(x²)+B/x+1/(10-x)
100/(x²)(10-x)=[10(10-x)+Bx(10-x)+x²)]/(x²(10-x)
100/(x²)(10-x)=[100-10x+10Bx-Bx²+x²]/(x²(10-x)
multiply by x²(10-x) and simplify
100=100+(10B-10)x+(1-B)x²
100+0x+0x²=100+(10B-10)x+(1-B)x²
coefficient of x must be 0
10B-10=0
10B=10
B=1
coefficient of x²must be 0
1-B=0
B=1
so 100/(x²)(10-x)=10/(x²)+1/x+1/(10-x)
is this correct?

[astarmathsandphysics]

I think so