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).
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