1. ## Complex fraction

I am not sure if i entered this correctly

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

2. 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...

3. ## Another try

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

4. 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:

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

5. ## Clarification

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

Thanks

6. ## Another try

Rational expressions

I have to simplify and reduce the following

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

Chester

7. 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...

8. ## shorter "quicker" work

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

9. ## 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?

10. 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

11. 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

12. 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