How do i find the range for

x+4/x+2.
I know to find range i need to solve the equation. But how do i do that?

Question

How do i find the range for 

x+4/x+2. 
I know to find range i need to solve the equation. But how do i do that?

anonymous · Answer

oh range, not domain, sorry

anonymous · Answer

you have a couple choices for finding the range.  the easiest is to think
a number is only one if the numerator and denominator are equal 
in this case you have $x+4$ in the numerator and  $x+2$ in the denominator and since it is not possible for $x+4$ to be equal to $x+2$ this sucker is never equal 1

ohmath123 · Answer

I know the domain is all real numbers except -2 right? @satellite73

anonymous · Answer

yes

anonymous · Answer

your other choice, much less fun than thinking, is to try to solve $$y=\frac{x+4}{x+2}$$ for $x$

anonymous · Answer

that will give you the inverse function
find the domain of the inverse function, that will be the range of this one

ganeshie8 · Answer

You may use componendo and dividendo to solve $x$ here

anonymous · Answer

@ganeshie8 lets keep it clean please

anonymous · Answer

actually i had to look that up to see what it meant !

ganeshie8 · Answer

it is actually more cleaner than the mess that we get by doing cross multiplication, grouping, and isolating

anonymous · Answer

expand!

ganeshie8 · Answer

just want to let the op know that there is something called "componendo and dividendo"
i don't want him to master this method in this thread haha

anonymous · Answer

dang i have to look it up again and try it myself then!

ganeshie8 · Answer

https://brilliant.org/wiki/componendo-and-dividendo/