Write the partial fraction decomposition of the following ra

Write the partial fraction decomposition of the following rational expression. -5x - 7 / (x - 5)^2 -5x - 7 / (x - 5)^2 =

Solution

given question is (-5x -7 ) / (x-5)^2

here the power of x in the numerator is 1

and the power of x in the denominator is 2

hence we can divide the question into partial fraction

the partial fraction of (-5x -7 ) / (x-5)^2 = A/(x-5) + B / (x-5)^2 [ here A and B are constants ]

(-5x -7 ) / (x-5)^2 = A/(x-5) + B / (x-5)^2   

(-5x -7 ) / (x-5)^2 = [ A(x-5) + B ] / (x-5)^2

-5x -7 = [ A(x-5) + B ]

-5x -7 = Ax -5A+B

now comparing the x coffient on left and right hand side

-5 = A

so A =-5

now comparing the constants

-5A+B = -7

-5(-5) +B=-7

25 +B =-7

B = -7 -25

B =-32

so the partial fraction of (-5x -7 ) / (x-5)^2 is -5/(x-5) -32 / (x-5)^2

(-5x -7 ) / (x-5)^2 =   -5/(x-5) -32 / (x-5)^2

I hope you understand it! if you have any doubts comment here.