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## anonymous one year ago Simplify 1 / (1+a^n) + 1/(1+a^-n)

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1. freckles

hint: multiply that second fraction by a^n/a^n

2. anonymous

Thanks but does it cancel out th denominater for the second fraction

3. freckles

$1 \cdot a_n=? \\ (1+a^{-n}) \cdot a_n=1 \cdot a_n +a^{-n} \cdot a^{n} =?$

4. anonymous

Wouldn't it be 1+a as the denimontar

5. freckles

those one n's were suppose to be exponents (not subscipts)

6. freckles

$1 \cdot a^n=a^n \\ (1+a^{-n}) \cdot a^n=1 \cdot a^n+a^{-n} a^{n} \text{ by distributive law } \\ \text{ now do you know law of exponents? }$

7. freckles

if you have the same base and you are multiplying what do you do with the exponents ?

8. anonymous

Add

9. freckles

$(1+a^{-n})a^n=a^n+a^{-n+n}=?$

10. freckles

-n+n=?

11. anonymous

0

12. freckles

right and a^0=?

13. anonymous

One

14. freckles

$\frac{1}{1+a^{n}}+\frac{a^n}{1+a^{n}}=?$

15. freckles

you see you have the same denominator

16. freckles

now you can write as one fraction

17. freckles

$\frac{1+a^{n}}{1+a^{n}}=?$

18. anonymous

1

19. freckles

right and this is of coursing assuming a>0

20. freckles

a could be less than 0 depending on n we could say a lot about the domain restrictions lol

21. freckles

but I'm sure they are just looking for 1

22. anonymous

Ok tysm

23. freckles

np

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