Express (16x^2 + 4x^3)/(x^3 + 2x^2 - 8x) + 12x/(x-2) as one fraction in its simplest form.

Answer: 16x/(x - 2)

Start with the numerator of the first fraction, 16x² + 4x³ , take a factor of 4x² out to get 4x²(4 + x). Then look at the denominator of the fraction, x³ + 2x² - 8x, immediately you can take out a factor of x to get, x(x² + 2x - 8) which you can then factorise to get x(x - 2)(x + 4). From this you can see that x(x + 4) can be removed from the numerator and denominator to leave 4x/(x - 2). Then since the two fractions now have the same denominator you can just add the numerators together, 4x + 12x = 16x, giving the answer 16x/(x - 2).