Simplify each complex fraction. Reduce each answer to
lowest terms.
ab+b^2/4ab^ 5
_______________
a+b/6a^2b^2
Well, it is easily changed to..
(ab+b)(6a^2b^2)/(a+b)(4ab^5)
I assume you can handle it from there. We will be happy to critique your work.
To simplify the given complex fraction, we can divide it into two separate fractions first:
Numerator: ab + b^2
Denominator: 4ab^5
Next, simplify the second fraction:
Numerator: a + b
Denominator: 6a^2b^2
Now, let's simplify each fraction separately.
For the first fraction:
The numerator contains two terms, ab and b^2. There aren't any common factors between these two terms, so we cannot simplify it further.
The denominator contains two terms, 4ab^5. Again, there aren't any common factors between these terms.
So, the first fraction remains unchanged.
ab + b^2
__________
4ab^5
For the second fraction:
The numerator contains two terms, a and b. Just like before, there aren't any common factors between these terms, so we cannot simplify it further.
The denominator contains two terms, 6a^2b^2. Again, there aren't any common factors between these terms.
So, the second fraction remains unchanged.
a + b
_______
6a^2b^2
Finally, the simplified complex fraction would be:
(ab + b^2) / (4ab^5)
_____________________
(a + b) / (6a^2b^2)
To divide complex fractions, we can multiply the first fraction by the reciprocal of the second fraction:
(ab + b^2) / (4ab^5) * (6a^2b^2) / (a + b)
Now, let's simplify this expression:
(ab + b^2) * (6a^2b^2) / (4ab^5 * (a + b))
Multiplying the numerators gives us:
6a^3b^2 + 6a^2b^3
Multiplying the denominators gives us:
4ab^6 * (a + b)
Now simplify the final expression:
(6a^3b^2 + 6a^2b^3) / (4ab^6 * (a + b))
At this point, we cannot simplify the expression further as there are no common factors between the numerator and denominator.
So, the simplified and reduced form of the complex fraction is:
(6a^3b^2 + 6a^2b^3) / (4ab^6 * (a + b))