everybody
Doing partial fraction decomposition and need help finding the answer to this using equating coefficents

3x-8=A(x-1)+B(x-5)

Question

everybody
Doing partial fraction decomposition and need help finding the answer to this using equating coefficents

3x-8=A(x-1)+B(x-5)

anonymous · Answer

put $x=1$ get 
$$-5=-4B$$ pretty much instantly

anonymous · Answer

but i want to solve it the long way by equating coefficients and i don't know how

anonymous · Answer

that is the simple way to do it, equatiing like coefficients is the donkey way, but we can do that if you like

anonymous · Answer

yes do do :D

anonymous · Answer

$$3x-8=A(x-1)+B(x-5)$$ multiply out on the right 
$$3x-8=Ax-A+Bx-5B$$

anonymous · Answer

combine like terms on the right 
$$3x-8=(A+B)x-A-5B$$

anonymous · Answer

that means $$A+B=3\
-A-5B=-8$$

anonymous · Answer

satellite come back to my aueastion i am not sure

anonymous · Answer

then solve that system of equations
add and get 
$$-4B=-5$$ which (hate to say i told you so) i got in one second in my head in line one above

anonymous · Answer

pleaase

anonymous · Answer

thank you satellite :)

anonymous · Answer

yw