# Help in simplifying

• Jan 7th 2009, 05:31 AM
AlgebraicallyChallenged
Help 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=

• Jan 7th 2009, 05:57 AM
earboth
Quote:

Originally Posted by AlgebraicallyChallenged
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=

Do you mean:

$\dfrac1{\frac1a} + \dfrac1b=$ If so:

$\dfrac1{\frac1a} + \dfrac1b= a+ \dfrac1b = \dfrac{ab}b + \dfrac1b =\dfrac{ab+1}b$
• Jan 7th 2009, 12:10 PM
Math Major
Quote:

Originally Posted by AlgebraicallyChallenged
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=

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, 12:42 PM
Soroban
Hello, AlgebraicallyChallenged!

Quote:

Simplify: . $\frac{1}{\frac{1}{a} + \frac{1}{b}}$
Multiply by $\frac{ab}{ab}$

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