Answer:
8x+19/(x+8)(x-1)= 5/(x+8) + 3/(x-1)
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)