Divide ( x^2 - 49 ) / x^2 y^3 ÷ ( x^2 - 14x + 49 ) / 3 x^2 y^3

Interchange the top and bottom of the second fractional expression to get:

(x² - 49)/x²y³ * 3x²y³/(x² - 14x + 49)

Then, by factoring each expression, we obtain:

(x - 7)(x + 7)/x²y³ * 3x²y³/(x - 7)²

Reduce the common factors of x - 7 and x²y³:

(x + 7)/1 * 3/(x - 7)

So by multiplying these fractional expressions altogether, we obtain:

3(x + 7)/(x - 7)

I hope this helps!

(x^2 - 49)..............(x^2 - 14x + 49)
________ ÷___________________; factor
x^2 y^3..................3x^2 y ^3

(x + 7)(x - 7).........(x - 7)(x - 7)
__________ ÷ ________________; flip the second fraction and use multiplication
x^2 y^3..................3x^2 y^3

(x+7)(x - 7)..............3x^2 y^3
_________ * __________________; make into one fraction
x^2 y^3................(x - 7)(x - 7)

(x + 7)(x - 7)*(3x^2 y^3)
___________________; simplify
(x^2 y^3) * (x - 7)(x - 7)

(x^2 - 49)(3x^2 y^3)
____________________: multiply
(x^2 y^3)(x^2 - 14x + 49)

3x^4y^3 - 147x^2y^3
________________________; factor
x^4y^3 - 14x^3y^3 + 49x^2y^3

3x^2y^3(x^2 - 49)
__________________; factor further
x^2y^3(x^2 - 14x + 49)

3x^2y^3(x - 7)(x + 7)
_________________; cancel common terms
x^2y^3(x - 7)(x - 7)

3x^2y^3(x + 7)
____________; simplify
x^2y^3(x - 7)

3(x+7)
_____ <-----------------Answer
(x - 7)

Blessings