How do you express #(-2x-3)/(x^2-x) # in partial fractions?

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Answer 1 · 2016-02-20T09:53:58

#3/x-5/(x-1)#

To write algebraic expression #(−2x−3)/(x^2−x)#,

we first factorize #(x^2−x)# i.e. #x(x−1)#.

Hence partial fractions will be of he type

#A/x+B/(x-1)# or #(Ax-A+Bx)/(x(x-1))# or

#((A+B)x-A)/(x(x-1))#

Hence #A+B=-2#

and #-A=-3# i.e. #A=3# and #B=-5#

Hence partial fractions are

#3/x-5/(x-1)#