How do you write the partial fraction decomposition of the rational expression # (3x + 2) / [(x - 1)(x + 4)]#?

1 Answer
Jan 2, 2016

#(3x+2)/((x-1)(x+4)) = 1/(x-1) + 2/(x+4)#

Explanation:

Since the denominator already in the factor form we can rewrite it as

# (3x+2)/((x-1)(x+4)) = A/(x-1) + B/(x+4)#

Multiply both sides by the LCD to get

#3x+ 2 = A (x+4) + B(x-1)#

Multiple the expression to get

# 3x+ 2 = Ax + 4A + Bx -B#

Set up the system of equation like this

#x: " " " " A + B = 3#
#x^0 " " " " 4A -B = 2#

Solve system by elimination method

#A + B = 3#

#4A -B = 2#

#5 A " " = 5"#

#=>A= 1#

Solve for B

#(1) + B = 3 => B = 2#

Partial fraction of #(3x+2)/((x-1)(x+4)) = 1/(x-1) + 2/(x+4)#