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!

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