Question

4а/а^2b : 5ab/(3a-3b)

Answer 1

$\frac{4a}{a^2b}:\frac{5ab}{3a-3b}\\\frac{4}{ab}*\frac{3a-3b}{5ab}=\frac{12(a-b)}{5a^2b^2}$

Answer 2

To simplify the expression, we can start by multiplying both the numerator and denominator of the first fraction by (3a - 3b) and both the numerator and denominator of the second fraction by a^2b:

(4a/ a^2b) * ((3a - 3b)/(3a - 3b)) : (5ab / (a^2b)) * ((a^2b)/(3a - 3b))

Simplifying the numerators and denominators, we get:

(12a^2 - 12ab)/(a^3b^2) : (5a)/(3 - 3b)

Now we can flip the second fraction and multiply it by the first:

(12a^2 - 12ab)/(a^3b^2) * (3 - 3b)/(5a)

Simplifying further, we get:

(4a - 4b)/(a^2b) * (3 - 3b)/(5a) = (-4(a-b))/(a^2b) * 3(1-b)/(5a) = -12(a-b)(1-b)/(5a^2b)

Therefore, the simplified expression is -12(a-b)(1-b)/(5a^2b).