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)

since proposition states that a number is greater than 25, if is true then the number must actually be greater than 25.

this implies that all possible options, except 24, can be accepted

(x, y)→(x − 8, y − 7)

step-by-step explanation:

enjoy!