Divide.

5x/x^2+2x / 30x^2/x+2

1 answer

To divide these fractions, we need to multiply the first fraction by the reciprocal of the second fraction.

First fraction: 5x/(x^2 + 2x)
Second fraction: 30x^2/(x + 2)

Reciprocal of the second fraction: (x + 2)/30x^2

Now, we can multiply the first fraction by the reciprocal of the second fraction:

5x/(x^2 + 2x) * (x + 2)/(30x^2)

To simplify this expression, we can cancel terms in the numerator and denominator that are the same:

(5x * (x + 2)) / ((x^2 + 2x) * 30x^2)
= (5x^2 + 10x) / (30x^3 + 60x^2)
= 5x(x + 2) / 30x^2(x + 2)

Finally, we can cancel the common factor of (x + 2) in the numerator and the denominator:

= 5x / 30x^2
= 1 / 6x

Therefore, the division of the given fractions is 1 / 6x.