## anonymous 3 years ago Help- find the limit of:

1. anonymous

$\lim_{x \rightarrow 2} \left( \frac{ 6 }{ x^2+2x-8 } \right)+\left(\frac{ x-6 }{ x^2-4} \right)$

2. anonymous

so I found that $\lim_{x \rightarrow 2} \left( \frac{ 6 }{ (x+4)(x-2) } \right)+\left( \frac{ x-6 }{ (x+2)(x-2) } \right)$ Now what?????

3. anonymous

now subsitute 2 in place of x

4. anonymous

it will be 6/0. error. I can't do that yet.

5. anonymous

1/0 = infinity

6. anonymous

sorry 1/3. I see the next step in the book but I don't understand how they got to it. I will write it up.

7. anonymous

$\lim_{x \rightarrow 2}\left( \frac{ 6(x+2)+(x-6)(x+4) }{ (x+4)(x-2)(x+2) } \right)$

8. anonymous

they took the LCM in this step

9. anonymous

ok. Can you explain that part to me? I don't seem to get it.

10. anonymous

write all the terms in denominator if some term is repeating more then once , just write it one time. like in this case on one side u have (x+4)(x−2) and on other side (x+2)(x−2) so write them all in denominator but (x-2) is written twice so u will just write it one time

11. anonymous

ok but what about the numerator? How did they get to that part?

12. anonymous

ok now move back a step and see see what u had in denominator before . u had (x+4)(x−2) right?

13. anonymous

so you compare the old denominator with new numerator whichever is the common denominator u cancel them and whatever is left u multiply it with numerator

14. anonymous

|dw:1353067137453:dw|

15. anonymous

|dw:1353067229340:dw|

16. anonymous

|dw:1353067272848:dw|

17. anonymous

|dw:1353067293846:dw|

18. anonymous

are you getting what i am doing?

19. anonymous

yes, so basically you devide the entire equation the the common denoiminator and then solve from there. I think I got it. Let me see if it works out.

20. Zarkon

$\lim_{x \rightarrow 2} \left[\left( \frac{ 6 }{ (x+4)(x-2) } \right)+\left( \frac{ x-6 }{ (x+2)(x-2) } \right)\right]$ $\lim_{x \rightarrow 2} \left[\frac{x+2}{x+2}\left( \frac{ 6 }{ (x+4)(x-2) } \right)+\frac{x+4}{x+4}\left( \frac{ x-6 }{ (x+2)(x-2) } \right)\right]$

21. anonymous

thnk