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How can i write a rational function with absolute values as a piecewise function, for example $$f(x)= \frac{|x+1|}{|x+2|}$$

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  • $\begingroup$ You just have to form the cases $x>-1,-1\ge x>-2,-2>x$, like always. $\endgroup$ – Shubham Johri Feb 5 at 4:08
  • $\begingroup$ thank you !! :) $\endgroup$ – Nick Kakl Feb 5 at 4:17
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Guide:

$$\frac{|x+1|}{|x+2|}=\left| \frac{x+1}{x+2}\right|$$

Hence, you just have to figure out when does $\frac{x+1}{x+2}\ge 0.$

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  • $\begingroup$ thanks a lot :D $\endgroup$ – Nick Kakl Feb 5 at 4:20

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