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## Compgroupmail Group Title Help- find the limit of: one year ago one year ago

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1. Compgroupmail Group Title

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

2. Compgroupmail Group Title

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. nubeer Group Title

now subsitute 2 in place of x

4. Compgroupmail Group Title

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

5. nubeer Group Title

1/0 = infinity

6. Compgroupmail Group Title

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. Compgroupmail Group Title

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

8. nubeer Group Title

they took the LCM in this step

9. Compgroupmail Group Title

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

10. nubeer Group Title

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. Compgroupmail Group Title

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

12. nubeer Group Title

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

13. nubeer Group Title

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. nubeer Group Title

|dw:1353067137453:dw|

15. nubeer Group Title

|dw:1353067229340:dw|

16. nubeer Group Title

|dw:1353067272848:dw|

17. nubeer Group Title

|dw:1353067293846:dw|

18. nubeer Group Title

are you getting what i am doing?

19. Compgroupmail Group Title

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 Group Title

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

21. Compgroupmail Group Title

thnk