1/x^2-9x-10

Question

Having some issues with this problem.

 

1/x^2-9x-10

 

Write the form of the partial-fraction decomposition.

 

Use  A, and B,  for the constants.

 

 

 

Do not solve for constants.

Answer 1

1/x^2 -9x-10

now factors of x² -9x-10 = (x-10)(x+1)

 

so 1/ x² -9x-10 = A/ (x-10) + B/ (x+1),

if you want to solve,

 1= A(x+1) +B (x-10)

1= x(A+B) +A -10B

so A+B= 0   ...eq 1, A-10B =1... eq 2

substract eq 1 from eq 2,

 

-11B=1, B= -1/11    A=1/11

1/x² -9x-10 = 1/11(x-10) -1/11(x+1)