# How do you express #1 / ((x+5)^2 (x-1)) # in partial fractions?

##### 1 Answer

Sep 30, 2016

#### Explanation:

#1/((x+5)^2(x-1)) = A/(x+5)^2 + B/(x+5) + C/(x-1)#

Multiplying both sides of this equation by

#1/(x-1) = A+B(x+5)+(C(x+5)^2)/(x-1)#

Now let

#A = 1/((-5)-1) = -1/6#

Multiplying both sides of the first equation by

#1/(x+5)^2 = (A(x-1))/(x+5)^2 + (B(x-1))/(x+5) + C#

Now let

#C = 1/((1)+5)^2 = 1/36#

Going back to the first equation and making a common denominator we find:

#1/((x+5)^2(x-1)) = A/(x+5)^2 + B/(x+5) + C/(x-1)#

#color(white)(1/((x+5)^2(x-1))) = (A(x-1)+B(x-1)(x+5)+C(x+5)^2)/((x+5)^2(x-1))#

So equating the coefficients of

#B = -C = -1/36#