Question

(a+c)/ac ∙ (5ac^2)/(c^2- a^2 )

Answer 1

$\dfrac{a+c}{ac}\cdot \dfrac{5ac^2}{c^2-a^2}=\dfrac{a+c}{ac}\cdot \dfrac{5ac^2}{(c-a)(c+a)}=\dfrac{5c}{c-a}$

Answer 2

To simplify the expression ((a+c)/ac) * (5ac^2)/(c^2 - a^2), we can first simplify each individual fraction and then perform the multiplication.

Let's start by simplifying the first fraction ((a+c)/ac):

((a+c)/ac) = (a+c) / (ac)

Now let's simplify the second fraction (5ac^2)/(c^2 - a^2):

(5ac^2)/(c^2 - a^2) = (5ac^2)/[(c+a)(c-a)]

Now, let's multiply the two simplified fractions:

((a+c)/ac) * (5ac^2)/(c^2 - a^2) = [(a+c) / (ac)] * [(5ac^2)/[(c+a)(c-a)]]

To multiply the fractions, we can cancel out common factors between the numerator and denominator:

[(a+c) * 5ac^2] / [(ac) * (c+a)(c-a)]

Simplifying further:

[5ac(a+c)] / [ac(c^2 - a^2)]

Next, we can cancel out the common factors of ac:

[5(a+c)] / (c^2 - a^2)

So, the simplified form of the expression ((a+c)/ac) * (5ac^2)/(c^2 - a^2) is [5(a+c)] / (c^2 - a^2).