Complex fraction

**Chester** · July 31st 2006, 07:08 PM

I am not sure if i entered this correctly

$ \frac {{ab+b^2}{4ab^5}}{{a+b}{6a^2b^4}} $

**Quick** · July 31st 2006, 07:10 PM

Originally Posted by Chester

I am not sure if i entered this correctly

math]
\frac {{ab+b^2}{4ab^5}}{{a+b}{6a^2b^4}}
[/tex]

maybe you're trying to say:
$ \frac{\frac{ab+b^2}{4ab^5}}{\frac{a+b}{6a^2b^4}} $
but that seems silly, with the bracket you left out your expression is:
$ \frac {{ab+b^2}{4ab^5}}{{a+b}{6a^2b^4}} $
but I don't understand...

**Chester** · July 31st 2006, 07:13 PM

$ \frac{ \frac{ab+b^2}{4ab^5} }{ \frac{a+b}{6a^2b^4}} $

**Quick** · July 31st 2006, 07:14 PM

Originally Posted by Chester

$ \frac{ \frac{ab+b^2}{4ab^5} }{ \frac{a+b}{6a^2b^4}} $

now you're going to need to clarify, are you saying:

$\frac{ab+b^2}{4ab^5} \div \frac{a+b}{6a^2b^4}$

**Chester** · July 31st 2006, 07:16 PM

Sorry,
I was trying to get the code to work. That is what i am saying. I have to simplify and reduce.

Thanks

**Chester** · July 31st 2006, 07:27 PM

Rational expressions

I have to simplify and reduce the following

$ \frac{ \frac{ab+b^2}{4ab^5} }{ \frac{a+b}{6a^2b^4}} $

Chester

**Quick** · July 31st 2006, 07:31 PM

Originally Posted by Chester

Sorry,
I was trying to get the code to work. That is what i am saying. I have to simplify and reduce.

Thanks

$ \frac{ab+b^2}{4ab^5} \div \frac{a+b}{6a^2b^4} $

switch the division sign to multiplication: $\frac{ab+b^2}{4ab^5} \times \frac{6a^2b^4}{a+b}$

multiply: $\frac{(ab+b^2)(6a^2b^4)}{(4ab^5)(a+b)}$

seperate: $\frac{ab+b^2}{a+b} \times \frac{6a^2b^4}{4ab^5}$

divide: $\frac{ab+b^2}{a+b} \times \frac{6a}{4b}$

multiply: $\frac{6a(ab+b^2)}{4b(a+b)}$

multiply: $\frac{6a^2b+6b^2a}{4ab+4b^2}$

split: $\frac{6a^2b}{4ab+4b^2}+\frac{6b^2a}{4ab+4b^2}$

simplify: $\frac{6a^2b}{4b(b+a)}+\frac{6b^2a}{4b(b+a)}$

simplify: $\frac{3a^2}{2(b+a)}+\frac{3ab}{2(b+a)}$

add: $\frac{3a^2+3ab}{2(b+a)}$

combine: $\frac{3a(a+b)}{2(b+a)}$

seperate: $\frac{3a}{2}\times\frac{a+b}{b+a}$

simplify: $\frac{3a}{2}\times1$

simplify: $\frac{3a}{2}$

I might have done more work than necessary, but I got the job done...

**Quick** · July 31st 2006, 07:35 PM

Originally Posted by Quick

switch the division sign to multiplication: $\frac{ab+b^2}{4ab^5} \times \frac{6a^2b^4}{a+b}$

multiply: $\frac{(ab+b^2)(6a^2b^4)}{(4ab^5)(a+b)}$

seperate: $\frac{ab+b^2}{a+b} \times \frac{6a^2b^4}{4ab^5}$

simplify: $\frac{b(a+b)}{a+b} \times \frac{6a}{4b}$

simplify: $b \times \frac{3a}{2b}$

multiply: $\frac{3ab}{2b}$

simplify: $\frac{3a}{2}$

**Chester** · July 31st 2006, 07:57 PM

I would like to solve this by finding the LCD and simplifying.

I think the LCD will be 12a^2b^5

Is that the corect start?

**topsquark** · August 1st 2006, 03:56 AM

Originally Posted by Chester

I would like to solve this by finding the LCD and simplifying.

I think the LCD will be 12a^2b^5

Is that the corect start?

Yes, that will work.

-Dan

**Quick** · August 1st 2006, 07:48 AM

Originally Posted by Chester

I would like to solve this by finding the LCD and simplifying.

I think the LCD will be 12a^2b^5

Is that the corect start?

division and multiplication doesn't require an LCD

**topsquark** · August 1st 2006, 08:00 AM

Originally Posted by Quick

division and multiplication doesn't require an LCD

No, it isn't required, but the standard method to simplify a complex fraction is to multiply the numerator and denominator by the LCD of the denominators of the "lesser" fractions. (I'm not sure what the standard terminology is here.) You can, of course, use other methods.

-Dan

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