# Find out domain and range

## Homework Statement

y = $$\frac{1}{(x-1)(x+2)}$$

find out the domain and range

ans: y<= -4/9 or y>0

$$x~E~R~-\{-2,1\}$$

## The Attempt at a Solution

I know the solution and I used this methoD:

y(x^2 + x -2) =1 (where $$y\neq0$$ )

when x is real, the discriminant

y^2 -4y(-2y-1) >=0 (where $$y\neq0$$ )

9y^2 + 4y >= 0 (where $$y\neq0$$ )

y(9y +4) >= 0 (where $$y\neq0$$ )

y<= -4/9 or y>0

My request is ... plz use some other easy method to illustrate this problem.. I want to know other methods of solving this same problem.. plz help.

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Forum $ignature: www.lingouist.blogspot.com[/URL] Last edited by a moderator: ## Answers and Replies This is the simplest way that I know of. If graphing is simple enough, you can try. tiny-tim Science Advisor Homework Helper Welcome to PF! ## Homework Statement y = $$\frac{1}{(x-1)(x+2)}$$ find out the domain and range Hi sinjan.j! Welcome to PF! Easy method: It looks nearly symmetric … so adjust it to make it symmetric! Hint: the range will be the same even if you make a substitution for x. Try w = x - a, where you choose a to make 1/(x-1)(x+2) symmetric in w. simpler method = calculator Thanx everbody ================================================== ================== Forum$ignature: www.lingouist.blogspot.com[/URL]

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