Simplify each complex fraction. Reduce each answer to lowest terms.
ab + b²
4ab
______________
a + b
6a²b
I only see one fraction, and don't understand why you have "stacked" terms in the numerator and denominator.
Try typing the fractions on a single line, using parentheses and brackets where necessary.
To simplify the given complex fraction, we need to simplify both the numerator and the denominator separately and then divide them.
Let's start with simplifying the numerator (ab + b²) / 4ab:
1. First, factor out the common term "b" from both "ab" and "b²":
(ab + b²) = b(a + b)
2. Now, we have (b(a + b)) / 4ab
Next, let's simplify the denominator (a + b) / 6a²b:
1. There are no common factors to factor out, so we leave it as it is.
2. The denominator is already in its simplest form.
Now that we have simplified the numerator and denominator separately, we can divide them to obtain our final answer:
(b(a + b)) / 4ab ÷ (a + b) / 6a²b
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
(b(a + b)) / 4ab × 6a²b / (a + b)
Simplifying further, we can cancel out the common factors:
(b(a + b)) / (2ab) × 3a / 1
Now, multiply the numerators and denominators:
3ab(a + b) / (2ab)
Finally, cancel out the common factors of "ab":
3(a + b) / 2
So, the simplified complex fraction is (3(a + b)) / 2.