# Complex fraction

• Jul 31st 2006, 07:08 PM
Chester
Complex fraction
I am not sure if i entered this correctly

$\displaystyle \frac {{ab+b^2}{4ab^5}}{{a+b}{6a^2b^4}}$
• Jul 31st 2006, 07:10 PM
Quick
Quote:

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:
$\displaystyle \frac{\frac{ab+b^2}{4ab^5}}{\frac{a+b}{6a^2b^4}}$
but that seems silly, with the bracket you left out your expression is:
$\displaystyle \frac {{ab+b^2}{4ab^5}}{{a+b}{6a^2b^4}}$
but I don't understand...
• Jul 31st 2006, 07:13 PM
Chester
Another try
$\displaystyle \frac{ \frac{ab+b^2}{4ab^5} }{ \frac{a+b}{6a^2b^4}}$
• Jul 31st 2006, 07:14 PM
Quick
Quote:

Originally Posted by Chester
$\displaystyle \frac{ \frac{ab+b^2}{4ab^5} }{ \frac{a+b}{6a^2b^4}}$

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

$\displaystyle \frac{ab+b^2}{4ab^5} \div \frac{a+b}{6a^2b^4}$
• Jul 31st 2006, 07:16 PM
Chester
Clarification
Sorry,
I was trying to get the code to work. That is what i am saying. I have to simplify and reduce.

Thanks
• Jul 31st 2006, 07:27 PM
Chester
Another try
Rational expressions

I have to simplify and reduce the following

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

Chester
• Jul 31st 2006, 07:31 PM
Quick
Quote:

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

Quote:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

I might have done more work than necessary, but I got the job done...
• Jul 31st 2006, 07:35 PM
Quick
shorter "quicker" work
Quote:

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

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

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

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

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

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

simplify: $\displaystyle \frac{3a}{2}$
• Jul 31st 2006, 07:57 PM
Chester
Lcd
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?
• Aug 1st 2006, 03:56 AM
topsquark
Quote:

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
• Aug 1st 2006, 07:48 AM
Quick
Quote:

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
• Aug 1st 2006, 08:00 AM
topsquark
Quote:

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