What is the partial fraction decomposition of
8x+19/(x+8)(x-1)?

8x+19/(x+8)(x-1)= 5/(x+8) +  3/(x-1)

Step-by-step explanation:

Step one:

given the expression

8x+19/(x+8)(x-1)

in partial fraction the expression is

8x+19/(x+8)(x-1)= A/(x+8) +  B/(x-1)

8x+19/(x+8)(x-1)= A(x-1)+B(x+8)/(x+8)(x-1)

equating the numerator we have

8x+19=A(x-1)+B(x+8)1

to find A put x=-8 in eqn 1

8(-8)+19=A(-8-1)+B(-8+8)

-64+19=-9A

-45=-9A

A=45/9

A=5

to find B put x=1 in eqn 1

8(1)+19=A(1-1)+B(1+8)

8+19=9B

27=9B

B=27/9

B=3

The partial fraction decomposition

8x+19/(x+8)(x-1)= 5/(x+8) +  3/(x-1)

  or  

step-by-step explanation:

if the four friends split the cost, p, of the pizza evenly, then each friend pays one-fourth of the cost of the pizza.

the expression is   or