How do you differentiate #f(x)= (x^2-x+2)/ (x- 1 )# using the quotient rule?

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Answer 1 · 2018-05-30T17:22:27

#f'(x)=1-2/((x-1)²)#

#f(x)=(x²-x+2)/(x-1)#

#=((x-1)²+x+1)/(x-1)#

#=(x-1)^(cancel(2)^(color(red)(=1)))/cancel((x-1))+(x+1)/(x-1)#

#f(x)=x-1+(x+1)/(x-1)#

Also, using quotient rule : #d/dx (u(x))/(v(x))=(u'v-uv')/(v²)#, there :
#u=x+1#

#v=x-1#

#u'=1#

#v'=1#

So:
#f'(x)=1+(cancel(x)-1-(cancel(x)+1))/((x-1)²)#

#f'(x)=1-2/((x-1)²)#

\0/ here's our answer!