Question

divide and simplify.
\\(\frac{a + b}{ab} div \frac{a^2 - b^2}{5a^4b}\\)
\\(\frac{a + b}{ab} div \frac{a^2 - b^2}{5a^4b} = square\\)

Explanation:

Step1: Recall division of fractions rule

To divide two fractions, we multiply the first fraction by the reciprocal of the second fraction. So, $\frac{a + b}{ab} \div \frac{a^2 - b^2}{5a^4b}$ becomes $\frac{a + b}{ab} \times \frac{5a^4b}{a^2 - b^2}$.

Step2: Factor the difference of squares

We know that $a^2 - b^2$ can be factored as $(a + b)(a - b)$ using the difference of squares formula $x^2 - y^2=(x + y)(x - y)$. So now our expression is $\frac{a + b}{ab} \times \frac{5a^4b}{(a + b)(a - b)}$.

Step3: Cancel out common factors

We can cancel out the common factors $(a + b)$ from the numerator and the denominator, and also cancel out $ab$ from the denominator of the first fraction and the numerator of the second fraction. After canceling, we have $\frac{5a^4b}{ab(a - b)}$ with $(a + b)$ canceled, then canceling $ab$ gives $\frac{5a^3}{a - b}$.

Answer:

$\frac{5a^3}{a - b}$