Good morning I tried to simplify the problem below and I am getting some weird results can anyone help me break this down ( simplify in detail )

1/ 1/a + 1/b=

thank you in advance.

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- Jan 7th 2009, 04:31 AMAlgebraicallyChallengedHelp in simplifying
Good morning I tried to simplify the problem below and I am getting some weird results can anyone help me break this down ( simplify in detail )

1/ 1/a + 1/b=

thank you in advance. - Jan 7th 2009, 04:57 AMearboth
- Jan 7th 2009, 11:10 AMMath Major

1/1/a is the same thing as writing 1 divided by 1/a. When we divide by a fraction, we multiply by its reciprocal, so the operation becomes 1 * a which is just a.

Now we have a + 1/b. In order to add these two, we have to have a common denominator. Since b is the lowest common denominator, multiply both the numerator and denominator of all terms by b.

(ab)/b + 1/b = (ab+1)/b - Jan 7th 2009, 11:42 AMSoroban
Hello, AlgebraicallyChallenged!

Quote:

Simplify: .$\displaystyle \frac{1}{\frac{1}{a} + \frac{1}{b}} $

. . $\displaystyle \frac{ab}{ab}\cdot\frac{1}{\dfrac{1}{a}+\dfrac{1}{ b}} \;=\;\frac{ab(1)}{{\color{red}\rlap{/}}ab\left(\dfrac{1}{{\color{red}\rlap{/}}a}\right) + a{\color{red}\rlap{/}}b\left(\dfrac{1}{{\color{red}\rlap{/}}b}\right)} $ . $\displaystyle =\;\;\frac{ab}{b + a}$