Chain Rule followed by Quotient Rule

[Lime]

u = (x^2 + 5) / (x - 1)

How do you get from this:

(1/u) * [{(x - 1)(2x) - (x^2 + 5)} / {(x - 1)^2}]

To this:

(x - 1)/(x^2 + 5) * (x^2 - 2x - 5) / (x - 1)^2

...

Does (1/u) = (x - 1)/(x^2 + 5) ???

 

[stapel]

u = (x^2 + 5) / (x - 1)

Does (1/u) = (x - 1)/(x^2 + 5)?

Yes.

Eliz.

 

[Lime]

How?

 

[galactus]

Quotient rule: \(\displaystyle \L\\\frac{f(x)}{g(x)}\)

\(\displaystyle \L\\\frac{g(x)f'(x)-f(x)g'(x)}{(g'(x))^{2}}\)

\(\displaystyle \L\\\frac{(x-1)(2x)-(x^{2}+5)(1)}{(x-1)^{2}}\)

\(\displaystyle \L\\=\frac{x^{2}-2x-5}{(x-1)^{2}}\)