How do you differentiate $f (x) = \frac{x + 5}{x - 7}$ $f(x)= (x+5)/ (x- 7 )$ using the quotient rule?

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Answer 1 · 2016-01-07T13:49:33

$f'(x)=-12/(x-7)^2$

Given:

$f(x)=(N(x))/(D(x))$

$f'(x)=(N'(x)*D(x)-D'(x)*N(x))/((D(x))^2)$

Then:

$f'(x)=(1*(x-7)-1*(x+5))/(x-7)^2=(cancel(x)-7cancel(-x)-5)/(x-7)^2=$
$=-12/(x-7)^2$

How do you differentiate f(x)= (x+5)/ (x- 7 )f(x)=x+5x−7f(x)= (x+5)/ (x- 7 ) using the quotient rule?