Divide the following rational expressions and simplify the result

When you divide fractions, you change the division sign to a multiplication sign and flip the second fraction. Factor the x^2 - 25 into (x+5)(x-5) and the (x-5) cancels out with the denominator of the other fraction, leaving (x+5)(4x+14)/5x(x+3). When you FOIL all that out, you're left with 4x^2+34x+70/5x^2+15x.  That's as simplified as it's going to get. The values of x that make the denominator undefined are x = 0, x = -3