High School Honors Algebra Factoring

[tobycutie]

I was having trouble getting the correctanswer for this problem. If you could tell me what I am doing wrong it would be greatly appreciated. Thanks!!!

Simplify
a^-1 + (ab)^-1
(a+b)^-1

1+1
a ab
1
a+b

To eliminate the complex fraction, I then multiplied by the LCD, ab(a+b) which gave me

b(a+b)+(a+b)
ab

(a+b)^2That is the correct answer
ab

Any help is greatly appreciated!!!

 

[garf]

Would you please check?, I got
(a+2b+1)/ab
garf

 

[Deleted member 4993]

I was having trouble getting the correctanswer for this problem. If you could tell me what I am doing wrong it would be greatly appreciated. Thanks!!!

Simplify
a^-1 + (ab)^-1
(a+b)^-1

1+1
a ab
1
a+b

To eliminate the complex fraction, I then multiplied by the LCD, ab(a+b) which gave me

b(a+b)+(a+b)
ab

(a+b)^2That is the correct answer
ab

Any help is greatly appreciated!!!

As posted your work is correct.

However, if the actual problem was:

\(\displaystyle \frac{a^{-1}+b^{-1}}{(a+b)^{-1}}\)

Then you'll get the book's answer.

 

[garf]

Would you please check?, I got
(a+2b+1)/ab
garf

I am sorry, I made a mistake, I got:
(a+b)(b+1)/ab,
I did not check your work,
garf

 

[tobycutie]

Thank you for your help!! I believe the book made an error because there is no possible way to get the answer listed. Thank you again it was much apprectiated!!