## Bananas1234 one year ago Simplify and identify the domain. -5/5x + 15 times 2(x + 2)/x^2 - 4

1. rajat97

to identify the domain, we need to see at which points, the function is undefined so the function is undefined at three points. those points are -3,2 and -2 the function is defined and exists at all real numbers except these three. thus the domain is all real numbers except -3,-2,2

2. rajat97

hello Bananas1234 is it right??

3. UsukiDoll

I think everyone needs a mandatory course in latex or something. I can't read this.

4. UsukiDoll

rajat, you're right for -2,2, and -3 will make the denominator 0. assuming that this is the right equation.

5. Bananas1234

idk what latex is. and i agree with the -2, 2 and -3 but what about the simplify part?

6. Bananas1234

@UsukiDoll

7. anonymous

factor both denominators, then cancel common terms

8. rajat97

look at the denominators

9. rajat97

the numbers at which the denominators become zero are the numbers that will be excluded from the domain

10. Bananas1234

|dw:1433046092010:dw|

11. UsukiDoll

-5/5x + 15 times 2(x + 2)/x^2 - 4 $\frac{-5}{5x+15} \times \frac{2(x+2)}{x^2-4}$

12. UsukiDoll

if we can pull that 5 out on the first denominator and then make sure that $x^2-4 = (x+2)(x-2)$ omg latex come on. x^2-4 = (x+2)(x-2) cancel out some of the terms... you should be able to cancel out 2 of them

13. UsukiDoll

sorry my end is bugged... need to refresh

14. UsukiDoll

$\frac{-5}{5(x+3)} \times \frac{2(x+2)}{(x+2)(x-2)}$ do you see anything that needs to be canceled out?

15. UsukiDoll

the common terms are 5 and x+2... since I can see them on the numerator and denominator we can cancel it out.

16. UsukiDoll

$\frac{-1}{(x+3)} \times \frac{2}{(x-2)}$ and since we're not dealing with addition, we can just multiply this through. $\frac{-2}{(x+3)(x-2)}$

17. Bananas1234

Thanks